Question: Simplify: \dfrac{x}{x²+2xy+y²} + \dfrac{y}{x²-y²}
Solution:
Given,
= \dfrac{x}{x²+2xy+y²} + \dfrac{y}{x²-y²}
= \dfrac{x}{(x+y)²} + \dfrac{y}{(x)² - (y)²}
= \dfrac{x}{(x+y)(x+y)} + \dfrac{y}{(x+y)(x-y)}
= \dfrac{x(x-y) + y(x+y)}{(x+y)(x+y)(x-y)}
= \dfrac{x² -xy +xy +y²}{(x+y)(x² -y²)}
= \dfrac{x² +y²}{(x+y)(x² -y²)}
= Answer
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