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Factorisation Using Algebraic Identities

Simplify x2...

Question

Simplify $\frac{x^{2} - 3 x + 2}{x^{2} - 1} =$

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Solution

$\frac{x^{2} - 3 x + 2}{x^{2} - 1}$

$= \frac{x^{2} - 2 x - x + 2}{x^{2} - {(1)}^{2}}$

$= \frac{x (x - 2) - 1 (x - 2)}{(x + 1) (x - 1)}$

$[a^{2} - b^{2} = (a + b) (a - b)]$

$= \frac{(x - 2)}{(x + 1)}$

$\frac{x^{2} - 3 x + 2}{x^{2} - 1} = \frac{x - 2}{x + 1}$

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