Exercise algebra.manipulation.rational.simplify

Description
simplify a rational expression (with a variable in a divisor)

Derivations

1.

7/(2*x)+3/(5*x)

⇒ algebra.equations.rational.rational-scale

35/(10*x)+6/(10*x)

⇒ algebra.equations.rational.rational-plus

41/(10*x)

2.

3/(2*x)+2/(3*x)

⇒ algebra.equations.rational.rational-scale

9/(6*x)+4/(6*x)

⇒ algebra.equations.rational.rational-plus

13/(6*x)

3.

4/(5*x)-2/(3*x)

⇒ algebra.equations.rational.rational-scale

12/(15*x)-10/(15*x)

⇒ algebra.equations.rational.rational-plus

2/(15*x)

4.

2/(7*x)-1/(4*x)

⇒ algebra.equations.rational.rational-scale

8/(28*x)-7/(28*x)

⇒ algebra.equations.rational.rational-plus

1/(28*x)

5.

5/(6*a)+3/(7*a)

⇒ algebra.equations.rational.rational-scale

35/(42*a)+18/(42*a)

⇒ algebra.equations.rational.rational-plus

53/(42*a)

6.

3/(8*a)+5/(3*a)

⇒ algebra.equations.rational.rational-scale

9/(24*a)+40/(24*a)

⇒ algebra.equations.rational.rational-plus

49/(24*a)

7.

7/(2*a)-2/(3*a)

⇒ algebra.equations.rational.rational-scale

21/(6*a)-4/(6*a)

⇒ algebra.equations.rational.rational-plus

17/(6*a)

8.

9/(5*a)-1/(2*a)

⇒ algebra.equations.rational.rational-scale

18/(10*a)-5/(10*a)

⇒ algebra.equations.rational.rational-plus

13/(10*a)

9.

1/x+1/y

⇒ algebra.equations.rational.rational-scale

y/(x*y)+x/(x*y)

⇒ algebra.equations.rational.rational-plus

(y+x)/(x*y)

10.

2/(3*x)+1/(2*y)

⇒ algebra.equations.rational.rational-scale

4*y/(6*x*y)+3*x/(6*x*y)

⇒ algebra.equations.rational.rational-plus

(4*y+3*x)/(6*x*y)

11.

3/(x^2*y)-5/(2*x*y)

⇒ algebra.equations.rational.rational-scale

6/(2*x^2*y)-5*x/(2*x^2*y)

⇒ algebra.equations.rational.rational-plus

(6-5*x)/(2*x^2*y)

12.

2/(x*y)-7/(5*y)

⇒ algebra.equations.rational.rational-scale

10/(5*x*y)-7*x/(5*x*y)

⇒ algebra.equations.rational.rational-plus

(10-7*x)/(5*x*y)

13.

2/a-3/b

⇒ algebra.equations.rational.rational-scale

2*b/(a*b)-3*a/(a*b)

⇒ algebra.equations.rational.rational-plus

(2*b-3*a)/(a*b)

14.

4/(3*a)-2/(5*b)

⇒ algebra.equations.rational.rational-scale

20*b/(15*a*b)-6*a/(15*a*b)

⇒ algebra.equations.rational.rational-plus

(20*b-6*a)/(15*a*b)

15.

2/(a*b)+4/(3*a)

⇒ algebra.equations.rational.rational-scale

6/(3*a*b)+4*b/(3*a*b)

⇒ algebra.equations.rational.rational-plus

(6+4*b)/(3*a*b)

16.

7/(4*a)+3/(4*b)

⇒ algebra.equations.rational.rational-scale

7*b/(4*a*b)+3*a/(4*a*b)

⇒ algebra.equations.rational.rational-plus

(7*b+3*a)/(4*a*b)

17.

3+1/(2*x)

⇒ algebra.equations.rational.to-rational

6*x/(2*x)+1/(2*x)

⇒ algebra.equations.rational.rational-plus

(6*x+1)/(2*x)

18.

2*x+3/(5*x)

⇒ algebra.equations.rational.to-rational

10*x^2/(5*x)+3/(5*x)

⇒ algebra.equations.rational.rational-plus

(10*x^2+3)/(5*x)

19.

5/(2*x)-3

⇒ algebra.equations.rational.to-rational

5/(2*x)-6*x/(2*x)

⇒ algebra.equations.rational.rational-plus

(5-6*x)/(2*x)

20.

3-5/(7*x)

⇒ algebra.equations.rational.to-rational

21*x/(7*x)-5/(7*x)

⇒ algebra.equations.rational.rational-plus

(21*x-5)/(7*x)

21.

5/(3*a)+1

⇒ algebra.equations.rational.to-rational

5/(3*a)+3*a/(3*a)

⇒ algebra.equations.rational.rational-plus

(5+3*a)/(3*a)

22.

4*a+3/(2*a)

⇒ algebra.equations.rational.to-rational

8*a^2/(2*a)+3/(2*a)

⇒ algebra.equations.rational.rational-plus

(8*a^2+3)/(2*a)

23.

2*a-1/(3*a)

⇒ algebra.equations.rational.to-rational

6*a^2/(3*a)-1/(3*a)

⇒ algebra.equations.rational.rational-plus

(6*a^2-1)/(3*a)

24.

7/(5*a)-2

⇒ algebra.equations.rational.to-rational

7/(5*a)-10*a/(5*a)

⇒ algebra.equations.rational.rational-plus

(7-10*a)/(5*a)

25.

5/(x+2)+4/(x+3)

⇒ algebra.equations.rational.rational-scale

(x+3)*5/((x+2)*(x+3))+(x+2)*4/((x+2)*(x+3))

⇒ algebra.equations.rational.rational-plus

((x+3)*5+(x+2)*4)/((x+2)*(x+3))

⇒ algebra.equations.linear.distr-times

(5*x+15+4*x+8)/((x+2)*(x+3))

⇒ algebra.equations.linear.merge

(9*x+23)/((x+2)*(x+3))

26.

3/(x-1)+2/(x+3)

⇒ algebra.equations.rational.rational-scale

(x+3)*3/((x-1)*(x+3))+(x-1)*2/((x-1)*(x+3))

⇒ algebra.equations.rational.rational-plus

((x+3)*3+(x-1)*2)/((x-1)*(x+3))

⇒ algebra.equations.linear.distr-times

(3*x+9+2*x-2)/((x-1)*(x+3))

⇒ algebra.equations.linear.merge

(5*x+7)/((x-1)*(x+3))

27.

4/(x+5)+2/(x-3)

⇒ algebra.equations.rational.rational-scale

(x-3)*4/((x+5)*(x-3))+(x+5)*2/((x+5)*(x-3))

⇒ algebra.equations.rational.rational-plus

((x-3)*4+(x+5)*2)/((x+5)*(x-3))

⇒ algebra.equations.linear.distr-times

(4*x-12+2*x+10)/((x+5)*(x-3))

⇒ algebra.equations.linear.merge

(6*x-2)/((x+5)*(x-3))

28.

3/(x-2)+2/(x-3)

⇒ algebra.equations.rational.rational-scale

(x-3)*3/((x-2)*(x-3))+(x-2)*2/((x-2)*(x-3))

⇒ algebra.equations.rational.rational-plus

((x-3)*3+(x-2)*2)/((x-2)*(x-3))

⇒ algebra.equations.linear.distr-times

(3*x-9+2*x-4)/((x-2)*(x-3))

⇒ algebra.equations.linear.merge

(5*x-13)/((x-2)*(x-3))

29.

4/(x+3)-6/(x+2)

⇒ algebra.equations.rational.rational-scale

(x+2)*4/((x+3)*(x+2))-(x+3)*6/((x+3)*(x+2))

⇒ algebra.equations.rational.rational-plus

((x+2)*4-(x+3)*6)/((x+3)*(x+2))

⇒ algebra.equations.linear.distr-times

(4*x+8-6*x-18)/((x+3)*(x+2))

⇒ algebra.equations.linear.merge

(-2*x-10)/((x+3)*(x+2))

30.

1/(x+5)-3/(x-4)

⇒ algebra.equations.rational.rational-scale

(x-4)/((x+5)*(x-4))-(x+5)*3/((x+5)*(x-4))

⇒ algebra.equations.rational.rational-plus

(x-4-(x+5)*3)/((x+5)*(x-4))

⇒ algebra.equations.linear.distr-times

(x-4-3*x-15)/((x+5)*(x-4))

⇒ algebra.equations.linear.merge

(-2*x-19)/((x+5)*(x-4))

31.

7/(x-3)-2/(x+1)

⇒ algebra.equations.rational.rational-scale

(x+1)*7/((x-3)*(x+1))-(x-3)*2/((x-3)*(x+1))

⇒ algebra.equations.rational.rational-plus

((x+1)*7-(x-3)*2)/((x-3)*(x+1))

⇒ algebra.equations.linear.distr-times

(7*x+7-2*x+6)/((x-3)*(x+1))

⇒ algebra.equations.linear.merge

(5*x+13)/((x-3)*(x+1))

32.

6/(x-1)-3/(x-2)

⇒ algebra.equations.rational.rational-scale

(x-2)*6/((x-1)*(x-2))-(x-1)*3/((x-1)*(x-2))

⇒ algebra.equations.rational.rational-plus

((x-2)*6-(x-1)*3)/((x-1)*(x-2))

⇒ algebra.equations.linear.distr-times

(6*x-12-3*x+3)/((x-1)*(x-2))

⇒ algebra.equations.linear.merge

(3*x-9)/((x-1)*(x-2))

33.

(x+1)/(x+2)+(x+2)/(x-3)

⇒ algebra.equations.rational.rational-scale

(x-3)*(x+1)/((x+2)*(x-3))+(x+2)*(x+2)/((x+2)*(x-3))

⇒ algebra.equations.rational.rational-plus

((x-3)*(x+1)+(x+2)*(x+2))/((x+2)*(x-3))

⇒ algebra.equations.linear.distr-times

(x^2-2*x-3+x^2+4*x+4)/((x+2)*(x-3))

⇒ algebra.equations.linear.merge

(2*x^2+2*x+1)/((x+2)*(x-3))

34.

(x-2)/(x+3)+(x-1)/(x+2)

⇒ algebra.equations.rational.rational-scale

(x+2)*(x-2)/((x+3)*(x+2))+(x+3)*(x-1)/((x+3)*(x+2))

⇒ algebra.equations.rational.rational-plus

((x+2)*(x-2)+(x+3)*(x-1))/((x+3)*(x+2))

⇒ algebra.equations.linear.distr-times

(x^2-4+x^2+2*x-3)/((x+3)*(x+2))

⇒ algebra.equations.linear.merge

(2*x^2-7+2*x)/((x+3)*(x+2))

35.

(x+3)/(x-1)+(x+2)/(x-4)

⇒ algebra.equations.rational.rational-scale

(x-4)*(x+3)/((x-1)*(x-4))+(x-1)*(x+2)/((x-1)*(x-4))

⇒ algebra.equations.rational.rational-plus

((x-4)*(x+3)+(x-1)*(x+2))/((x-1)*(x-4))

⇒ algebra.equations.linear.distr-times

(x^2-x-12+x^2+x-2)/((x-1)*(x-4))

⇒ algebra.equations.linear.merge

(2*x^2-14)/((x-1)*(x-4))

36.

(x-4)/(x+5)+(x-2)/(x-3)

⇒ algebra.equations.rational.rational-scale

(x-3)*(x-4)/((x+5)*(x-3))+(x+5)*(x-2)/((x+5)*(x-3))

⇒ algebra.equations.rational.rational-plus

((x-3)*(x-4)+(x+5)*(x-2))/((x+5)*(x-3))

⇒ algebra.equations.linear.distr-times

(x^2-7*x+12+x^2+3*x-10)/((x+5)*(x-3))

⇒ algebra.equations.linear.merge

(2*x^2-4*x+2)/((x+5)*(x-3))

37.

(x-1)/(x+1)-(x+2)/(x-2)

⇒ algebra.equations.rational.rational-scale

(x-2)*(x-1)/((x+1)*(x-2))+(x+1)*(-x-2)/((x+1)*(x-2))

⇒ algebra.equations.rational.rational-plus

((x-2)*(x-1)+(x+1)*(-x-2))/((x+1)*(x-2))

⇒ algebra.equations.linear.distr-times

(x^2-3*x+2-x^2-3*x-2)/((x+1)*(x-2))

⇒ algebra.equations.linear.merge

-6*x/((x+1)*(x-2))

38.

(x+5)/(x+3)-(x+3)/(x+5)

⇒ algebra.equations.rational.rational-scale

(x+5)*(x+5)/((x+3)*(x+5))+(x+3)*(-x-3)/((x+3)*(x+5))

⇒ algebra.equations.rational.rational-plus

((x+5)*(x+5)+(x+3)*(-x-3))/((x+3)*(x+5))

⇒ algebra.equations.linear.distr-times

(x^2+10*x+25-x^2-6*x-9)/((x+3)*(x+5))

⇒ algebra.equations.linear.merge

(4*x+16)/((x+3)*(x+5))

39.

(x-1)/(x+2)-(x+4)/(x+1)

⇒ algebra.equations.rational.rational-scale

(x+1)*(x-1)/((x+2)*(x+1))+(x+2)*(-x-4)/((x+2)*(x+1))

⇒ algebra.equations.rational.rational-plus

((x+1)*(x-1)+(x+2)*(-x-4))/((x+2)*(x+1))

⇒ algebra.equations.linear.distr-times

(x^2-1-x^2-6*x-8)/((x+2)*(x+1))

⇒ algebra.equations.linear.merge

(-9-6*x)/((x+2)*(x+1))

40.

(x-3)/(x-1)-(x+2)/(x+4)

⇒ algebra.equations.rational.rational-scale

(x+4)*(x-3)/((x-1)*(x+4))+(x-1)*(-x-2)/((x-1)*(x+4))

⇒ algebra.equations.rational.rational-plus

((x+4)*(x-3)+(x-1)*(-x-2))/((x-1)*(x+4))

⇒ algebra.equations.linear.distr-times

(x^2+x-12-x^2-x+2)/((x-1)*(x+4))

⇒ algebra.equations.linear.merge

-10/((x-1)*(x+4))

41.

2*x/(x-1)+x/(x+2)

⇒ algebra.equations.rational.rational-scale

(x+2)*2*x/((x-1)*(x+2))+(x-1)*x/((x-1)*(x+2))

⇒ algebra.equations.rational.rational-plus

((x+2)*2*x+(x-1)*x)/((x-1)*(x+2))

⇒ algebra.equations.linear.distr-times

(2*x^2+4*x+x^2-x)/((x-1)*(x+2))

⇒ algebra.equations.linear.merge

(3*x^2+3*x)/((x-1)*(x+2))

42.

3*x/(x-4)+5*x/(x-2)

⇒ algebra.equations.rational.rational-scale

(x-2)*3*x/((x-4)*(x-2))+(x-4)*5*x/((x-4)*(x-2))

⇒ algebra.equations.rational.rational-plus

((x-2)*3*x+(x-4)*5*x)/((x-4)*(x-2))

⇒ algebra.equations.linear.distr-times

(3*x^2-6*x+5*x^2-20*x)/((x-4)*(x-2))

⇒ algebra.equations.linear.merge

(8*x^2-26*x)/((x-4)*(x-2))

43.

4*x/(x+2)-2*x/(x+1)

⇒ algebra.equations.rational.rational-scale

(x+1)*4*x/((x+2)*(x+1))-(x+2)*2*x/((x+2)*(x+1))

⇒ algebra.equations.rational.rational-plus

((x+1)*4*x-(x+2)*2*x)/((x+2)*(x+1))

⇒ algebra.equations.linear.distr-times

(4*x^2+4*x-2*x^2-4*x)/((x+2)*(x+1))

⇒ algebra.equations.linear.merge

2*x^2/((x+2)*(x+1))

44.

x/(x+5)-4*x/(x+6)

⇒ algebra.equations.rational.rational-scale

(x+6)*x/((x+5)*(x+6))-(x+5)*4*x/((x+5)*(x+6))

⇒ algebra.equations.rational.rational-plus

((x+6)*x-(x+5)*4*x)/((x+5)*(x+6))

⇒ algebra.equations.linear.distr-times

(x^2+6*x-4*x^2-20*x)/((x+5)*(x+6))

⇒ algebra.equations.linear.merge

(-3*x^2-14*x)/((x+5)*(x+6))

45.

(x^2+4*x-5)/(x^2+5*x-6)

⇒ algebra.equations.quadratic.nice-factors

(x^2+4*x-5)/((x-1)*(x+6))

⇒ algebra.equations.quadratic.nice-factors

(x-1)*(x+5)/((x-1)*(x+6))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= 1)]

(x+5)/(x+6)

46.

(x^2+2*x-8)/(x^2+10*x+24)

⇒ algebra.equations.quadratic.nice-factors

(x^2+2*x-8)/((x+4)*(x+6))

⇒ algebra.equations.quadratic.nice-factors

(x-2)*(x+4)/((x+4)*(x+6))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= -4)]

(x-2)/(x+6)

47.

(x^2-7*x+12)/(x^2+x-20)

⇒ algebra.equations.quadratic.nice-factors

(x^2-7*x+12)/((x-4)*(x+5))

⇒ algebra.equations.quadratic.nice-factors

(x-3)*(x-4)/((x-4)*(x+5))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= 4)]

(x-3)/(x+5)

48.

(x^2+7*x+12)/(x^2+5*x+6)

⇒ algebra.equations.quadratic.nice-factors

(x^2+7*x+12)/((x+2)*(x+3))

⇒ algebra.equations.quadratic.nice-factors

(x+3)*(x+4)/((x+2)*(x+3))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= -3)]

(x+4)/(x+2)

49.

(a^2-a-2)/(a^2+4*a-12)

⇒ algebra.equations.quadratic.nice-factors

(a^2-a-2)/((a-2)*(a+6))

⇒ algebra.equations.quadratic.nice-factors

(a+1)*(a-2)/((a-2)*(a+6))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= 2)]

(a+1)/(a+6)

50.

(a^2-3*a-10)/(a^2-a-20)

⇒ algebra.equations.quadratic.nice-factors

(a^2-3*a-10)/((a+4)*(a-5))

⇒ algebra.equations.quadratic.nice-factors

(a+2)*(a-5)/((a+4)*(a-5))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= 5)]

(a+2)/(a+4)

51.

(a^2-2*a-15)/(a^2-3*a-18)

⇒ algebra.equations.quadratic.nice-factors

(a^2-2*a-15)/((a+3)*(a-6))

⇒ algebra.equations.quadratic.nice-factors

(a+3)*(a-5)/((a+3)*(a-6))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= -3)]

(a-5)/(a-6)

52.

(a^2+a-2)/(a^2+3*a+2)

⇒ algebra.equations.quadratic.nice-factors

(a^2+a-2)/((a+1)*(a+2))

⇒ algebra.equations.quadratic.nice-factors

(a-1)*(a+2)/((a+1)*(a+2))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= -2)]

(a-1)/(a+1)

53.

(x^2-16)/(x^2+x-12)

⇒ algebra.equations.quadratic.nice-factors

(x^2-16)/((x-3)*(x+4))

⇒ algebra.equations.quadratic.nice-factors

(x+4)*(x-4)/((x-3)*(x+4))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= -4)]

(x-4)/(x-3)

54.

(x^2-2*x+1)/(x^2-1)

⇒ algebra.equations.quadratic.nice-factors

(x^2-2*x+1)/((x+1)*(x-1))

⇒ algebra.equations.quadratic.nice-factors

(x-1)^2/((x+1)*(x-1))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= 1)]

(x-1)/(x+1)

55.

(x^2-9)/(x^2+6*x+9)

⇒ algebra.equations.quadratic.nice-factors

(x^2-9)/(x+3)^2

⇒ algebra.equations.quadratic.nice-factors

(x+3)*(x-3)/(x+3)^2

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= -3)]

(x-3)/(x+3)

56.

(x^2-7*x+6)/(x^2-1)

⇒ algebra.equations.quadratic.nice-factors

(x^2-7*x+6)/((x+1)*(x-1))

⇒ algebra.equations.quadratic.nice-factors

(x-1)*(x-6)/((x+1)*(x-1))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= 1)]

(x-6)/(x+1)

57.

(2*p^2+8*p)/(p^2-16)

⇒ algebra.equations.quadratic.nice-factors

(2*p^2+8*p)/((p+4)*(p-4))

⇒ algebra.equations.quadratic.common-factor

2*p*(p+4)/((p+4)*(p-4))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (p /= -4)]

2*p/(p-4)

58.

(-p^2+5*p)/(p^2-10*p+25)

⇒ algebra.equations.quadratic.nice-factors

(-p^2+5*p)/(p-5)^2

⇒ algebra.equations.quadratic.common-factor

-p*(p-5)/(p-5)^2

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (p /= 5)]

-p/(p-5)

59.

(p^2-4)/(4*p^2+8*p)

⇒ algebra.equations.quadratic.common-factor

(p^2-4)/(4*p*(p+2))

⇒ algebra.equations.quadratic.nice-factors

(p+2)*(p-2)/(4*p*(p+2))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (p /= -2)]

(p-2)/(4*p)

60.

(p^2-12*p+36)/(p^2-6*p)

⇒ algebra.equations.quadratic.common-factor

(p^2-12*p+36)/(p*(p-6))

⇒ algebra.equations.quadratic.nice-factors

(p-6)^2/(p*(p-6))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (p /= 6)]

(p-6)/p

61.

(x^3+3*x^2+2*x)/(x^2+4*x+4)

⇒ algebra.equations.quadratic.nice-factors

(x^3+3*x^2+2*x)/(x+2)^2

⇒ algebra.equations.polynomial.factor-varpower

x*(x^2+3*x+2)/(x+2)^2

⇒ algebra.equations.quadratic.nice-factors

x*(x+1)*(x+2)/(x+2)^2

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= -2)]

x*(x+1)/(x+2)

⇒ algebra.equations.linear.distr-times

(x^2+x)/(x+2)

62.

(x^3+10*x^2+24*x)/(x^2+7*x+6)

⇒ algebra.equations.quadratic.nice-factors

(x^3+10*x^2+24*x)/((x+1)*(x+6))

⇒ algebra.equations.polynomial.factor-varpower

x*(x^2+10*x+24)/((x+1)*(x+6))

⇒ algebra.equations.quadratic.nice-factors

x*(x+4)*(x+6)/((x+1)*(x+6))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= -6)]

x*(x+4)/(x+1)

⇒ algebra.equations.linear.distr-times

(x^2+4*x)/(x+1)

63.

(x^2+5*x+6)/(x^3-x^2-6*x)

⇒ algebra.equations.polynomial.factor-varpower

(x^2+5*x+6)/(x*(x^2-x-6))

⇒ algebra.equations.quadratic.nice-factors

(x^2+5*x+6)/(x*(x+2)*(x-3))

⇒ algebra.equations.quadratic.nice-factors

(x+2)*(x+3)/(x*(x+2)*(x-3))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= -2)]

(x+3)/(x*(x-3))

64.

(x^2+3*x-4)/(x^3-6*x^2+5*x)

⇒ algebra.equations.polynomial.factor-varpower

(x^2+3*x-4)/(x*(x^2-6*x+5))

⇒ algebra.equations.quadratic.nice-factors

(x^2+3*x-4)/(x*(x-1)*(x-5))

⇒ algebra.equations.quadratic.nice-factors

(x-1)*(x+4)/(x*(x-1)*(x-5))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (x /= 1)]

(x+4)/(x*(x-5))

65.

(a^3+7*a^2+12*a)/(a^2+6*a+9)

⇒ algebra.equations.quadratic.nice-factors

(a^3+7*a^2+12*a)/(a+3)^2

⇒ algebra.equations.polynomial.factor-varpower

a*(a^2+7*a+12)/(a+3)^2

⇒ algebra.equations.quadratic.nice-factors

a*(a+3)*(a+4)/(a+3)^2

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= -3)]

a*(a+4)/(a+3)

⇒ algebra.equations.linear.distr-times

(a^2+4*a)/(a+3)

66.

(a^3+7*a^2+10*a)/(a^2-a-6)

⇒ algebra.equations.quadratic.nice-factors

(a^3+7*a^2+10*a)/((a+2)*(a-3))

⇒ algebra.equations.polynomial.factor-varpower

a*(a^2+7*a+10)/((a+2)*(a-3))

⇒ algebra.equations.quadratic.nice-factors

a*(a+2)*(a+5)/((a+2)*(a-3))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= -2)]

a*(a+5)/(a-3)

⇒ algebra.equations.linear.distr-times

(a^2+5*a)/(a-3)

67.

(a^2-9)/(a^3-4*a^2+3*a)

⇒ algebra.equations.polynomial.factor-varpower

(a^2-9)/(a*(a^2-4*a+3))

⇒ algebra.equations.quadratic.nice-factors

(a^2-9)/(a*(a-1)*(a-3))

⇒ algebra.equations.quadratic.nice-factors

(a+3)*(a-3)/(a*(a-1)*(a-3))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= 3)]

(a+3)/(a*(a-1))

68.

(a^2-2*a-15)/(a^3-3*a^2-10*a)

⇒ algebra.equations.polynomial.factor-varpower

(a^2-2*a-15)/(a*(a^2-3*a-10))

⇒ algebra.equations.quadratic.nice-factors

(a^2-2*a-15)/(a*(a+2)*(a-5))

⇒ algebra.equations.quadratic.nice-factors

(a+3)*(a-5)/(a*(a+2)*(a-5))

⇒ algebra.equations.rational.cancel-div, clipboard=[condition == (a /= 5)]

(a+3)/(a*(a+2))