Help me solve this equation, step by step? x / (x+1) - 5 / (x - 2) = 1?

Question

x / (x+1) - 5 / (x - 2) = 1

Answer 1

x/(x+1) - 5/(x-2) =1
multiply the first term by (x-2)/(x-2) and the second by (x+1)/(x+1)
x(x-2)/(x+1)(x-2) -5(x+1)/(x+1)(x-2)=1 You now have a common denominator
x(x-2)-5(x+1)/(x+1)(x-2)=1
(x^2-2x-5x-5)/(x^2+x-2x-2)=1
multiply both sides by the denominator
x^2-7x-5=x^2-x-2
subtract x^2 from both sides
-7x-5=-x-2 add x and 5 to both sides
-6x=3 x=-3/6 or x=-1/2

Checking the math
(-1/2)/(-1/2+1)-5/(-1/2-2)=1
(-1/2)/1/2-5/(-5/2)=1
-1-(-2)=1
1=1 it checks out.

Answer 2

x/(x+1) - 5/(x-2)=1
make the denominator common for all terms on the left to get
x(x-2)/(x-2)(x+1)-5(x+1)/(x+1)(x-2)=1
multiply
(x^2 -2x)/(x-2)(x+1) - (5x+5)/(x+1)(x-2)=1
add the terms with like denominators
(x^2 -2x -5x -5)/(x+1)(x-2)=1
multiply both sides by (x+1)(x-2)
x^2-2x-5x-5=(x+1)(x-2)
expand the right side
x^2-7x-5=x^2-x-2
simplify
x^2-x^2 -6x =5-2
simplify
-6x=3, then x = 3/-6 = -1/2
Check your answer by substituting -1/2 for x and solve
-1/2/(1/2) - 5/(-5/2) =-1+2 = 1

Answer 3

x / (x+1) - 5 / (x - 2) = 1
multiply through by (x-2)
x(x-2)/(x+1) - 5 = x-2
add 5 to both sides
x(x-2)/(x+1) = x+3
multiply through by (x+1)
x(x-2) = (x+3)(x+1)
simplify
x^2-2x = x^2+4x+3
subtract x^2 from both sides
-2x = 4x+3
subtract 4x from both sides
-6x = 3
divide through by -6 and reduce
x = -1/2

Check answer by plugging -1/2 for each x in the original equation -1 +2 = 1 its good.

Hope this helps :-)

Answer 4

x(x-2)-5(x+1) = (x+1)(x-2)

x^2 -2x -5x - 5 = x^2 -x -2

- 7x -5 = -x -2

- 6x = 3

x = -1/2

Answer 5

x.(x - 2) - 5.(x + 1) = (x + 1).(x - 2)
x² - 2x - 5x - 5 = x² - x - 2
-7x - 5 = - x - 2
- 3 = 6x
x = - 1/2

Answer 6

x / (x+1) - 5 / (x-2) = 1

[x (x-2) - 5 (x+1)]/(x+1)(x-2) = 1 [taking L.C.M]

x (x-2) - 5 (x+1) = (x+1)(x-2)

x^2 - 2x - 5x - 5 = x^2 - 2x + x -2 [ x^2 means x square]

x^2 - 7x - 5 = x^2 - x -2

x^2 -7x - x^2 + x -3 = 0 [ taking all to one side]

-6x - 3 =0

-6x = 3

x = 3 / -6

x = -1/2

Answer 7

x/(x+1) - 5/(x-2)=1
[x(x-2) -5(x+1)] / [(x+1)(x-2)] = 1
x(x-2) - 5(x+1)=(x+1)(x-2)
x²-2x -5x -5=x² -x -2
6x=-3
x=-1/2

Answer 8

x/(x+1) - 5/(x-2) = 1

[x(x-2) - 5(x+1)] / [(x+1) (x-2)] = 1

[x^2 - 2x -5x - 5] / [(x+1) (x-2)] = 1

[x^2 - 7x - 5] = (x+1) (x-2)

x^2 - 7x - 5 = x^2 - x - 2

6x = -3

x = -1/2

Answer 9

2(x+1)=3x-3 2x+2=3x-3 <= Distribute the 2 2x+5=3x <= Add 3 to both sides 5=x <= Subtract 2x from both sides

Answer 10

1. x(x-2)/(x-1)(x-2) - 5(x-1)/(x-1)(x-2) = 1
2. [x(x-2) - 5(x-1)] / [(x-1)(x-2)] = 1
3. [x^2 - 2x - 5x + 5] / [(x-1)(x-2)] = 1
4. [x^2 - 2x - 5x + 5] = [(x-1)(x-2)]
5. [x^2 - 2x - 5x + 5] = x^2 -2x -x + 2
6. [x^2 - 2x - 5x + 5] = x^2 - 3x +2
7. x^2 - 2x - 5x + 5 - x^2 + 3x - 2 = 0
8. -4x + 3 = 0
and do the rest yourself