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

The solution to (x/y+y/2+z/x)^2 is ((2x^2+xy^2+2zy)^2)/(4x^2y^2)

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

simplify

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

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

Solution steps

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

Simplify

\frac{x}{y} + \frac{y}{2} + \frac{z}{x} : \frac{2 x ^{2} + x y ^{2} + 2 zy}{2 x y}

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Simplify

(2 x y)^{2} : 4 x^{2} y^{2}

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

((\frac{a}{b})^{- 2})^{\frac{3}{4}}

csc^{2} (x) sin^{2} (x) + cot^{2} (x) - csc^{2} (x)

\frac{6}{10} \frac{\frac{x ^{2}}{6}}{10} x^{3} - 60 x^{2}

(a + 2 b)^{5}

\frac{( x ^{n} - 1 )}{( x - 1 )}

What is (x/y+y/2+z/x)^2 ?
The solution to (x/y+y/2+z/x)^2 is ((2x^2+xy^2+2zy)^2)/(4x^2y^2)