How do you solve \frac { x - 2} { x + 1} + 1= \frac { x - 1} { x + 1}x2x+1+1=x1x+1?

1 Answer
Jun 8, 2017

x = 0

Explanation:

1) Multiply both sides by x+1x+1 :

color(red)((x+1))((x-2)/(x+1)) + 1(x+1)(x+1)(x2x+1)+1(x+1) = color(red)((x+1))((x-1)/(x+1))(x+1)(x1x+1)

2) Cancel out like-terms
cancel(color(red)((x+1)))((x-2)/cancel((x+1))) + 1color(red)((x+1)) = color(red)(cancel((x+1)))((x-1)/cancel((x+1)))

3) Rewrite:
x-2+x+1=x-1

4) Combine like terms on left-hand side then add the 1 from the right-hand side
2x-1 = x-1
2x = x

5) Subtract the x from the right-hand side
2x color(red)(-x) = xcolor(red)(-x)
2x = 0

6) Divide by 2
x = 0