What is expand (x^2+(1+y)^2)/(xy) ?

The solution to expand (x^2+(1+y)^2)/(xy) is x/y+1/(xy)+2/x+y/x

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expand (x^2+(1+y)^2)/(xy)

expand

\frac{x ^{2} + ( 1 + y ) ^{2}}{x y}

\frac{x}{y} + \frac{1}{x y} + \frac{2}{x} + \frac{y}{x}

Solution steps

\frac{x ^{2} + ( 1 + y ) ^{2}}{x y}

Expand

x^{2} + (1 + y)^{2} : x^{2} + 1 + 2 y + y^{2}

= \frac{x ^{2} + 1 + 2 y + y ^{2}}{x y}

Apply the fraction rule:

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

\frac{x ^{2} + 1 + 2 y + y ^{2}}{x y} = \frac{x ^{2}}{x y} + \frac{1}{x y} + \frac{2 y}{x y} + \frac{y ^{2}}{x y}

= \frac{x ^{2}}{x y} + \frac{1}{x y} + \frac{2 y}{x y} + \frac{y ^{2}}{x y}

Cancel

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

= \frac{x}{y} + \frac{1}{x y} + \frac{2 y}{x y} + \frac{y ^{2}}{x y}

Cancel

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

= \frac{x}{y} + \frac{1}{x y} + \frac{2}{x} + \frac{y ^{2}}{x y}

Cancel

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

= \frac{x}{y} + \frac{1}{x y} + \frac{2}{x} + \frac{y}{x}

\frac{1}{N ( a - b N )}

((e^{x}) + (e^{- x}))^{2}

(2 x + y) H (2 x + y)

(x ln (x) + y ln (y)) e

\frac{4 x - 1}{2 ( 4 x + 1 )}

What is expand (x^2+(1+y)^2)/(xy) ?
The solution to expand (x^2+(1+y)^2)/(xy) is x/y+1/(xy)+2/x+y/x