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

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

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simplify (sqrt(x/y)+sqrt(y/x))^2

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Simplify

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

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

\frac{n ( 2 n - 1 ) ( 2 n + 1 )}{3}

\frac{x - 2}{( x + 2 ) ( x - 3 )}

\frac{x + 6}{x}

(y - 2)^{2}

\frac{( s - 1 ) ^{3}}{s ^{4}}

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