Evaluate
\frac{xy}{x+y}
Expand
\frac{xy}{x+y}
Share
Copied to clipboard
\frac{\frac{\left(x-y\right)^{2}}{x-y}}{\frac{x}{y}-\frac{y}{x}}
Factor the expressions that are not already factored in \frac{x^{2}+y^{2}-2xy}{x-y}.
\frac{x-y}{\frac{x}{y}-\frac{y}{x}}
Cancel out x-y in both numerator and denominator.
\frac{x-y}{\frac{xx}{xy}-\frac{yy}{xy}}
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}.
\frac{x-y}{\frac{xx-yy}{xy}}
Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, subtract them by subtracting their numerators.
\frac{x-y}{\frac{x^{2}-y^{2}}{xy}}
Do the multiplications in xx-yy.
\frac{\left(x-y\right)xy}{x^{2}-y^{2}}
Divide x-y by \frac{x^{2}-y^{2}}{xy} by multiplying x-y by the reciprocal of \frac{x^{2}-y^{2}}{xy}.
\frac{xy\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}
Factor the expressions that are not already factored.
\frac{xy}{x+y}
Cancel out x-y in both numerator and denominator.
\frac{\frac{\left(x-y\right)^{2}}{x-y}}{\frac{x}{y}-\frac{y}{x}}
Factor the expressions that are not already factored in \frac{x^{2}+y^{2}-2xy}{x-y}.
\frac{x-y}{\frac{x}{y}-\frac{y}{x}}
Cancel out x-y in both numerator and denominator.
\frac{x-y}{\frac{xx}{xy}-\frac{yy}{xy}}
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}.
\frac{x-y}{\frac{xx-yy}{xy}}
Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, subtract them by subtracting their numerators.
\frac{x-y}{\frac{x^{2}-y^{2}}{xy}}
Do the multiplications in xx-yy.
\frac{\left(x-y\right)xy}{x^{2}-y^{2}}
Divide x-y by \frac{x^{2}-y^{2}}{xy} by multiplying x-y by the reciprocal of \frac{x^{2}-y^{2}}{xy}.
\frac{xy\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}
Factor the expressions that are not already factored.
\frac{xy}{x+y}
Cancel out x-y in both numerator and denominator.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}