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


Related Notes and Solutions:

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