Solve xy/x+y*(1/x+1/y)

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

Evaluate

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Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and y is xy. Multiply \frac{1}{x} times \frac{y}{y}. Multiply \frac{1}{y} times \frac{x}{x}.

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

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

$$\frac{xy}{x+y}\times \frac{y+x}{xy}$$

Multiply \frac{xy}{x+y} times \frac{y+x}{xy} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out xy\left(x+y\right) in both numerator and denominator.

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Factor

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