Could somebody please help with this math problem?

Question

Find m so that this equation contains only one solution 
(x + 2)/(x - m)=(x + 1)/(x - 1) 

Answer 1

Given equaton is

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

Using cross multiplication

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

( x² + x - 2x - 2 ) = ( x² + x - mx - m )

x² - x - 2 =  x² + x ( 1 - m ) - m

Compare constant terms on both sides.

- 2 = - m

m = 2

Compare coefficients of x terms on both sides.

- 1 = 1 - m

m = 1 + 1

 m = 2

In both cases m value is same.

Solution is m = 2