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

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justaguide's profile pic

Posted on

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)

kanishkporwal's profile pic

Posted on

[(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

giorgiana1976's profile pic

Posted on

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)

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