# Fractions .Simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)].

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First, we'll write the numerators and denominators as distinct factors. For this reason, we'll determine the roots of the first numerator:

x^2 + 3x + 2 = 0

We'll apply quadratic formula:

x1 = [-3+sqrt(9 - 8)]/2

x1 = (-3+1)/2

x1 = -1

x2 = (-3-1)/2

x2 = -2

The equation will be written as:

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

We'll write the 2nd factor as a product:

x^2 - 4 = (x-2)(x+2)

We'll re-write the factorised expression:

[(x+1)(x+2)/(x-2)]*[(x-2)(x+2)/(x-1)]

We'll cancel common factors:

(x+1)(x+2)^2/(x-1)

We'll leave the factors as they are and the simplified expression is:

**(x+1)(x+2)^2/(x-1)**

We need to simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

[(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]

use x^2 - 4 = (x - 2)(x +2), also let's find the factors of x^2+3x+2

=> [(x^2 + 2x + x +2)/(x-2)]*[(x - 2)(x + 2)/(x-1)]

=> [(x + 2)(x + 1)/(x - 2)]*[(x - 2)(x + 2)/(x-1)]

cancel the common terms in the numerator and denominator

=> (x + 2)^2*(x + 1)/(x - 1)

**The simplified form of the given expression is (x + 2)^2*(x + 1)/(x - 1)**

[(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)].

[(x^2+2x+x+2)/(x-2)]*[(x+2)(x-2)/(x-1)]

[(x+1)(x+2)/(x-2)]*[(x+2)(x-2)/(x-1)]

[(x+2)^2*(x+1)]/(x-1)

This was all about how to simplify fractions