How do you solve \frac { x } { x - 1} = \frac { 2} { x - 1}xx1=2x1?

1 Answer
Apr 24, 2017

x=2x=2

Explanation:

x/(x-1)=2/(x-1)xx1=2x1

Since we have common denominators we can subtract without changing anything

Move 2/(x-1)2x1 to the other side of the equals sign as a negative

x/(x-1)-2/(x-1)=0xx12x1=0

This also equals

(x-2)/(x-1)=0x2x1=0

Multiply both sides by (x-1)(x1) to remove the denominator

cancel(x-1)((x-2)/cancel(x-1))=cancel(0(x-1))

x-2=0

x=2

VERIFY YOUR ANSWER

Since x=2,

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

((2))/((2)-1)=2/((2)-1)

2/1=2/1

2=2