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

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

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

expand

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

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

Solution steps

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

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

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

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

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

Cancel

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

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

Cancel

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

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

Cancel

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

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

\frac{1}{( y + 2 ) ( y - 5 ) ( y + 7 )}

\frac{( x ^{2} + 5 ) ^{3}}{6}

\frac{1 + x}{( 2 x + 1 ) ( x - 1 )}

x d y \cdot (y + 3) - d y (y + 3)

\frac{d}{d t} ((s) (6 t^{5} - 8 t + 5))

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