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

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Answer 1 · 2017-06-08T02:46:48

x = 0

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

#color(red)((x+1))((x-2)/(x+1)) + 1(x+1)# = #color(red)((x+1))((x-1)/(x+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