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Composite Function

Simplify: x...

Question

Simplify: $\frac{(x^{2} - 4) (x + 1)}{x^{2} + 3 x + 2}$

A

x + 1

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B

x + 2

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C

x - 1

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D

x - 2

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Solution

The correct option is D $x - 2$
$\frac{(x^{2} - 4) (x + 1)}{x^{2} + 3 x + 2}$
We know that $x^{2} - y^{2} = (x + y) (x - y)$
Factor of $x^{2} + 3 x + 2 = (x + 1) (x + 2)$
So, $\frac{(x^{2} - 4) (x + 1)}{x^{2} + 3 x + 2} = \frac{(x + 2) (x - 2) (x + 1)}{(x + 1) (x + 2)}$
$= x - 2$
$∴ \frac{(x^{2} - 4) (x + 1)}{x^{2} + 3 x + 2} = x - 2$

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