Clear of fractions and solve for x (x-3)/(x-1)=(x+1)/(x+2)

We'll cross multiply and we'll get the cleared
equation:

(x-1)(x+1) =
(x-3)(x+2)

We notice that we'll get a difference of 2
squares to the left side. We'll remove the brackets from the right
side:

x^2 - 1 = x^2 + 2x - 3x -
6

x^2 - 1 = x^2 - x - 6

We'll
remove the like terms and we'll get:

-1 = -x -
6

We'll shift all terms to the left
side:

x + 6 - 1 = 0

We'll
combine like terms:

x + 5 =
0

x = -5

The
solution of the equation is x = -5.