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

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

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

expand

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

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

Solution steps

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

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

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

Apply the fraction rule:

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

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

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

Cancel

\frac{x ^{2}}{x} : x

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

Cancel

\frac{2 x y}{x} : 2 y

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

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