What is expand (y(x^2+y^2)^2)/(x^5) ?

The solution to expand (y(x^2+y^2)^2)/(x^5) is y/x+(2y^3)/(x^3)+(y^5)/(x^5)

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expand (y(x^2+y^2)^2)/(x^5)

expand

\frac{y ( x ^{2} + y ^{2} ) ^{2}}{x ^{5}}

\frac{y}{x} + \frac{2 y ^{3}}{x ^{3}} + \frac{y ^{5}}{x ^{5}}

Solution steps

\frac{y ( x ^{2} + y ^{2} ) ^{2}}{x ^{5}}

(x^{2} + y^{2})^{2} = x^{4} + 2 y^{2} x^{2} + y^{4}

= \frac{y ( y ^{4} + 2 y ^{2} x ^{2} + x ^{4} )}{x ^{5}}

Expand

y (x^{4} + 2 y^{2} x^{2} + y^{4}) : y x^{4} + 2 y^{3} x^{2} + y^{5}

= \frac{y x ^{4} + 2 y ^{3} x ^{2} + y ^{5}}{x ^{5}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{y x ^{4} + 2 y ^{3} x ^{2} + y ^{5}}{x ^{5}} = \frac{y x ^{4}}{x ^{5}} + \frac{2 y ^{3} x ^{2}}{x ^{5}} + \frac{y ^{5}}{x ^{5}}

= \frac{y x ^{4}}{x ^{5}} + \frac{2 y ^{3} x ^{2}}{x ^{5}} + \frac{y ^{5}}{x ^{5}}

Cancel

\frac{y x ^{4}}{x ^{5}} : \frac{y}{x}

= \frac{y}{x} + \frac{2 y ^{3} x ^{2}}{x ^{5}} + \frac{y ^{5}}{x ^{5}}

Cancel

\frac{2 y ^{3} x ^{2}}{x ^{5}} : \frac{2 y ^{3}}{x ^{3}}

= \frac{y}{x} + \frac{2 y ^{3}}{x ^{3}} + \frac{y ^{5}}{x ^{5}}

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What is expand (y(x^2+y^2)^2)/(x^5) ?
The solution to expand (y(x^2+y^2)^2)/(x^5) is y/x+(2y^3)/(x^3)+(y^5)/(x^5)