Simplify: \(\frac{x^2 - y^2}{(x + y)^2} + \frac{(x - y)^2}{(3x + 3y)}\)
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Correct Answer: Option C
Explanation:
\(\frac{x^2 - y^2}{(x + y)^2} + \frac{(x - y)^2}{(3x + 3y)}\)
\(\frac{(x + y)(x - y)}{(x + y)(x + y)} + \frac{(x - y)(x - y)}{3(x + y)}\)
= \(\frac{3}{x - y}\)
\(\frac{x^2 - y^2}{(x + y)^2} + \frac{(x - y)^2}{(3x + 3y)}\)
\(\frac{(x + y)(x - y)}{(x + y)(x + y)} + \frac{(x - y)(x - y)}{3(x + y)}\)
= \(\frac{3}{x - y}\)