Solve (x/y+y/x+2)*1/(x+y)^2

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

Evaluate

$$\frac{1}{xy}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{x}{y} times \frac{x}{x}. Multiply \frac{y}{x} times \frac{y}{y}.

$$\left(\frac{xx}{xy}+\frac{yy}{xy}+2\right)\times \frac{1}{\left(x+y\right)^{2}}$$

Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, add them by adding their numerators.

$$\left(\frac{xx+yy}{xy}+2\right)\times \frac{1}{\left(x+y\right)^{2}}$$

Do the multiplications in xx+yy.

$$\left(\frac{x^{2}+y^{2}}{xy}+2\right)\times \frac{1}{\left(x+y\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{xy}{xy}.

$$\left(\frac{x^{2}+y^{2}}{xy}+\frac{2xy}{xy}\right)\times \frac{1}{\left(x+y\right)^{2}}$$

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

$$\frac{x^{2}+y^{2}+2xy}{xy}\times \frac{1}{\left(x+y\right)^{2}}$$

Multiply \frac{x^{2}+y^{2}+2xy}{xy} times \frac{1}{\left(x+y\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x+y\right)^{2} in both numerator and denominator.

$$\frac{1}{xy}$$

Expand

$$\frac{1}{xy}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{x}{y} times \frac{x}{x}. Multiply \frac{y}{x} times \frac{y}{y}.

$$\left(\frac{xx}{xy}+\frac{yy}{xy}+2\right)\times \frac{1}{\left(x+y\right)^{2}}$$

Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, add them by adding their numerators.

$$\left(\frac{xx+yy}{xy}+2\right)\times \frac{1}{\left(x+y\right)^{2}}$$

Do the multiplications in xx+yy.

$$\left(\frac{x^{2}+y^{2}}{xy}+2\right)\times \frac{1}{\left(x+y\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{xy}{xy}.

$$\left(\frac{x^{2}+y^{2}}{xy}+\frac{2xy}{xy}\right)\times \frac{1}{\left(x+y\right)^{2}}$$

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

$$\frac{x^{2}+y^{2}+2xy}{xy}\times \frac{1}{\left(x+y\right)^{2}}$$

Multiply \frac{x^{2}+y^{2}+2xy}{xy} times \frac{1}{\left(x+y\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x+y\right)^{2} in both numerator and denominator.

$$\frac{1}{xy}$$