x/(x²+2xy+y²) + y/(x²-y²) | Simplification of Rational Expressions | SciPiPupil

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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