Evaluate
\frac{2x\left(y-2x\right)}{2x+y}
Expand
\frac{2\left(xy-2x^{2}\right)}{2x+y}
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\frac{2xy\left(y-2x\right)\left(2x+y\right)}{\left(y+2x\right)^{2}y}
Divide \frac{2xy}{\left(y+2x\right)^{2}} by \frac{y}{\left(y-2x\right)\left(2x+y\right)} by multiplying \frac{2xy}{\left(y+2x\right)^{2}} by the reciprocal of \frac{y}{\left(y-2x\right)\left(2x+y\right)}.
\frac{2x\left(-2x+y\right)}{2x+y}
Cancel out y\left(2x+y\right) in both numerator and denominator.
\frac{-4x^{2}+2xy}{2x+y}
Use the distributive property to multiply 2x by -2x+y.
\frac{2xy\left(y-2x\right)\left(2x+y\right)}{\left(y+2x\right)^{2}y}
Divide \frac{2xy}{\left(y+2x\right)^{2}} by \frac{y}{\left(y-2x\right)\left(2x+y\right)} by multiplying \frac{2xy}{\left(y+2x\right)^{2}} by the reciprocal of \frac{y}{\left(y-2x\right)\left(2x+y\right)}.
\frac{2x\left(-2x+y\right)}{2x+y}
Cancel out y\left(2x+y\right) in both numerator and denominator.
\frac{-4x^{2}+2xy}{2x+y}
Use the distributive property to multiply 2x by -2x+y.
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}