We have (x-3)/(x-1)=(x+1)/(x+2), and we have to solve for x.

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

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

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

=> -x = 5

=> x = -5

**The required value of x = -5**

Q: (x - 3) / (x - 1) = (x + 1) / (x + 2)

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

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

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

=> x = - 5

Ans :- minus 5 (-5)

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.**