Evaluate
\frac{xy-2x-3y}{2\left(x+2\right)\left(x+y\right)}
Expand
\frac{xy-2x-3y}{2\left(x+2\right)\left(x+y\right)}
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\frac{-2x+xy-3y}{2x^{2}-2x-12}\times \frac{x^{2}-3x-2xy+6y}{x^{2}-xy-2y^{2}}
Combine x and -3x to get -2x.
\frac{-2x+xy-3y}{2x^{2}-2x-12}\times \frac{\left(x-3\right)\left(x-2y\right)}{\left(x+y\right)\left(x-2y\right)}
Factor the expressions that are not already factored in \frac{x^{2}-3x-2xy+6y}{x^{2}-xy-2y^{2}}.
\frac{-2x+xy-3y}{2x^{2}-2x-12}\times \frac{x-3}{x+y}
Cancel out x-2y in both numerator and denominator.
\frac{\left(-2x+xy-3y\right)\left(x-3\right)}{\left(2x^{2}-2x-12\right)\left(x+y\right)}
Multiply \frac{-2x+xy-3y}{2x^{2}-2x-12} times \frac{x-3}{x+y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-3\right)\left(xy-2x-3y\right)}{2\left(x-3\right)\left(x+2\right)\left(x+y\right)}
Factor the expressions that are not already factored.
\frac{xy-2x-3y}{2\left(x+2\right)\left(x+y\right)}
Cancel out x-3 in both numerator and denominator.
\frac{xy-2x-3y}{2x^{2}+2xy+4x+4y}
Expand the expression.
\frac{-2x+xy-3y}{2x^{2}-2x-12}\times \frac{x^{2}-3x-2xy+6y}{x^{2}-xy-2y^{2}}
Combine x and -3x to get -2x.
\frac{-2x+xy-3y}{2x^{2}-2x-12}\times \frac{\left(x-3\right)\left(x-2y\right)}{\left(x+y\right)\left(x-2y\right)}
Factor the expressions that are not already factored in \frac{x^{2}-3x-2xy+6y}{x^{2}-xy-2y^{2}}.
\frac{-2x+xy-3y}{2x^{2}-2x-12}\times \frac{x-3}{x+y}
Cancel out x-2y in both numerator and denominator.
\frac{\left(-2x+xy-3y\right)\left(x-3\right)}{\left(2x^{2}-2x-12\right)\left(x+y\right)}
Multiply \frac{-2x+xy-3y}{2x^{2}-2x-12} times \frac{x-3}{x+y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-3\right)\left(xy-2x-3y\right)}{2\left(x-3\right)\left(x+2\right)\left(x+y\right)}
Factor the expressions that are not already factored.
\frac{xy-2x-3y}{2\left(x+2\right)\left(x+y\right)}
Cancel out x-3 in both numerator and denominator.
\frac{xy-2x-3y}{2x^{2}+2xy+4x+4y}
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}