Solve (x+y)^2/xy+(x-y)^2/xy

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

Evaluate

$$\frac{2\left(x^{2}+y^{2}\right)}{xy}$$

Short Solution Steps

Since \frac{\left(x+y\right)^{2}}{xy} and \frac{\left(x-y\right)^{2}}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\left(x+y\right)^{2}+\left(x-y\right)^{2}}{xy}$$

Do the multiplications in \left(x+y\right)^{2}+\left(x-y\right)^{2}.

$$\frac{x^{2}+2xy+y^{2}+x^{2}-2xy+y^{2}}{xy}$$

Combine like terms in x^{2}+2xy+y^{2}+x^{2}-2xy+y^{2}.

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

Expand

$$\frac{2\left(x^{2}+y^{2}\right)}{xy}$$

Short Solution Steps

Since \frac{\left(x+y\right)^{2}}{xy} and \frac{\left(x-y\right)^{2}}{xy} have the same denominator, add them by adding their numerators.

$$\frac{\left(x+y\right)^{2}+\left(x-y\right)^{2}}{xy}$$

Do the multiplications in \left(x+y\right)^{2}+\left(x-y\right)^{2}.

$$\frac{x^{2}+2xy+y^{2}+x^{2}-2xy+y^{2}}{xy}$$

Combine like terms in x^{2}+2xy+y^{2}+x^{2}-2xy+y^{2}.

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