The correct option is D x yx+y Given, #160; x^2 y^2(x+y)^2 .We know, a^2 b^2=(a+b)(a b) .Then, x^2 y^2(x+y)^2 =(x+y)(x y)(x+y)^2 ...

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Algebraic Identities

Simplify: x...

Question

Simplify: $\frac{x^{2} - y^{2}}{(x + y)^{2}}$ .

\frac{x + y}{x - y}

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\frac{(x + y)^{2}}{x - y}

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\frac{x + y}{x^{2} - y^{2}}

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\frac{x - y}{x + y}

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Solution

The correct option is D $\frac{x - y}{x + y}$
Given, $\frac{x^{2} - y^{2}}{(x + y)^{2}}$ .

We know, $a^{2} - b^{2} = (a + b) (a - b)$ .

Then,
$\frac{x^{2} - y^{2}}{(x + y)^{2}}$

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

$= \frac{x - y}{x + y}$ .

Therefore, option $D$ is correct.

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