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Math Help - simplify help

  1. #1
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    simplify help

     <br />
(x+\frac{y^2}{x-y})/(\frac{x^3+y^3}{x^2-y^2})<br />

     <br />
(\frac {x}{x}+\frac{y^2}{x-y})/(\frac{x^3+y^3}{x^2-y^2})<br />

     <br />
\frac {x(x-y)+xy^2}{x(x-y)} \cdot \frac{(x-y)(x+y)}{(x+y)(x^2-xy+y^2)}<br />

    is this correcT? thank u
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  2. #2
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    Hello, jvignacio!

    Simplify: .  <br />
\left(x+\frac{y^2}{x-y}\right) \div \left(\frac{x^3+y^3}{x^2-y^2}\right)

    The first expression is: . \frac{x}{1}\cdot\frac{x-y}{x-y} \;+\;\frac{y^2}{x-y}\;=\;\frac{x(x-y) + y^2}{x-y} \;=\;\frac{x^2-xy+y^2}{x-y}

    The second expression is: . \frac{(x+y)(x^2-xy+y^2)}{(x-y)(x+y)} \;=\;\frac{x^2-xy+r^2}{x-y}

    The problem becomes: . \frac{x^2-xy+y^2}{x-y} \div \frac{x^2-xy+y^2}{x-y} \;=\;\frac{x^2-xy+y^2}{x-y}\cdot\frac{x-y}{x^2-xy+y^2} \;=\;\boxed{1}

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