What is (sqrt(x+5)-x/y)^2 ?

The solution to (sqrt(x+5)-x/y)^2 is (xy^2+5y^2-2xysqrt(x+5)+x^2)/(y^2)

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simplify (sqrt(x+5)-x/y)^2

simplify

(x + 5 - \frac{x}{y})^{2}

\frac{x y ^{2} + 5 y ^{2} - 2 x y x + 5 + x ^{2}}{y ^{2}}

Solution steps

(x + 5 - \frac{x}{y})^{2}

Apply Perfect Square Formula:

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

(x + 5 - \frac{x}{y})^{2} = (x + 5)^{2} - 2 x + 5 \frac{x}{y} + (\frac{x}{y})^{2}

= (x + 5)^{2} - 2 x + 5 \frac{x}{y} + (\frac{x}{y})^{2}

Simplify

(x + 5)^{2} - 2 x + 5 \frac{x}{y} + (\frac{x}{y})^{2} : \frac{x y ^{2} + 5 y ^{2} - 2 x + 5 x y + x ^{2}}{y ^{2}}

= \frac{x y ^{2} + 5 y ^{2} - 2 x + 5 x y + x ^{2}}{y ^{2}}

= \frac{x y ^{2} + 5 y ^{2} - 2 x y x + 5 + x ^{2}}{y ^{2}}

(2 x - 5) (3 x + 1)

(x - 1 + 1)^{2}

\frac{100 s + 1000}{s ( s ^{2} + 10 s + 1000 )}

\frac{\partial}{\partial x} ((x - 1)^{2}) + (y - 3)^{2}

(x - 1 + 2 i) (x - 1 - 2 i)

What is (sqrt(x+5)-x/y)^2 ?
The solution to (sqrt(x+5)-x/y)^2 is (xy^2+5y^2-2xysqrt(x+5)+x^2)/(y^2)