Evaluate
-\frac{x^{2}+y^{2}}{\left(x+y\right)^{2}}
Expand
-\frac{x^{2}+y^{2}}{\left(x+y\right)^{2}}
Share
Copied to clipboard
\frac{\left(y^{-2}x^{2}+1\right)x^{-2}}{\left(-y^{-2}x^{2}+1\right)x^{-2}}\times \frac{x-y}{x+y}
Factor the expressions that are not already factored in \frac{x^{-2}+y^{-2}}{x^{-2}-y^{-2}}.
\frac{y^{-2}x^{2}+1}{-y^{-2}x^{2}+1}\times \frac{x-y}{x+y}
Cancel out x^{-2} in both numerator and denominator.
\frac{y^{-2}\left(x^{2}+y^{2}\right)}{y^{-2}\left(-x^{2}+y^{2}\right)}\times \frac{x-y}{x+y}
Factor the expressions that are not already factored in \frac{y^{-2}x^{2}+1}{-y^{-2}x^{2}+1}.
\frac{x^{2}+y^{2}}{-x^{2}+y^{2}}\times \frac{x-y}{x+y}
Cancel out y^{-2} in both numerator and denominator.
\frac{\left(x^{2}+y^{2}\right)\left(x-y\right)}{\left(-x^{2}+y^{2}\right)\left(x+y\right)}
Multiply \frac{x^{2}+y^{2}}{-x^{2}+y^{2}} times \frac{x-y}{x+y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-y\right)\left(x^{2}+y^{2}\right)}{\left(x+y\right)\left(x-y\right)\left(-x-y\right)}
Factor the expressions that are not already factored.
\frac{x^{2}+y^{2}}{\left(x+y\right)\left(-x-y\right)}
Cancel out x-y in both numerator and denominator.
\frac{x^{2}+y^{2}}{-x^{2}-2xy-y^{2}}
Expand the expression.
\frac{\left(y^{-2}x^{2}+1\right)x^{-2}}{\left(-y^{-2}x^{2}+1\right)x^{-2}}\times \frac{x-y}{x+y}
Factor the expressions that are not already factored in \frac{x^{-2}+y^{-2}}{x^{-2}-y^{-2}}.
\frac{y^{-2}x^{2}+1}{-y^{-2}x^{2}+1}\times \frac{x-y}{x+y}
Cancel out x^{-2} in both numerator and denominator.
\frac{y^{-2}\left(x^{2}+y^{2}\right)}{y^{-2}\left(-x^{2}+y^{2}\right)}\times \frac{x-y}{x+y}
Factor the expressions that are not already factored in \frac{y^{-2}x^{2}+1}{-y^{-2}x^{2}+1}.
\frac{x^{2}+y^{2}}{-x^{2}+y^{2}}\times \frac{x-y}{x+y}
Cancel out y^{-2} in both numerator and denominator.
\frac{\left(x^{2}+y^{2}\right)\left(x-y\right)}{\left(-x^{2}+y^{2}\right)\left(x+y\right)}
Multiply \frac{x^{2}+y^{2}}{-x^{2}+y^{2}} times \frac{x-y}{x+y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-y\right)\left(x^{2}+y^{2}\right)}{\left(x+y\right)\left(x-y\right)\left(-x-y\right)}
Factor the expressions that are not already factored.
\frac{x^{2}+y^{2}}{\left(x+y\right)\left(-x-y\right)}
Cancel out x-y in both numerator and denominator.
\frac{x^{2}+y^{2}}{-x^{2}-2xy-y^{2}}
Expand the expression.
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}