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Factors of Algebraic Expressions and Factorisation

Simplify x2...

Question

Simplify $\frac{x^{2} + y^{2} - z^{2} + 2 x y}{x^{2} - y^{2} - z^{2} - 2 y z} .$

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Solution

Simplify $\frac{x^{2} + y^{2} - z^{2} + 2 x y}{x^{2} - y^{2} - z^{2} - 2 y z} = \frac{x^{2} + y^{2} + 2 x y - z^{2}}{x^{2} - [y^{2} + z^{2} + 2 y z]}$
$= \frac{(x + y)^{2} - z^{2}}{x^{2} - (y + z)^{2}} = \frac{((x + y) - z) (x + y + z)}{(x - (y + z)) (x + y + z)}$ $a^{2} - b^{2} = (a - b) (a + b)$
$= \frac{(x + y - z) (x + y + z)}{(x - y - z) (x + y + z)}$
$= \frac{x + y - z}{x - y - z}$

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