Evaluate
\frac{x^{2}-2x-2y^{2}+4y}{xy}
Expand
\frac{x^{2}-2x-2y^{2}+4y}{xy}
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\frac{x-2y}{x}\left(\frac{y}{y}+\frac{x-2}{y}\right)+1
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.
\frac{x-2y}{x}\times \frac{y+x-2}{y}+1
Since \frac{y}{y} and \frac{x-2}{y} have the same denominator, add them by adding their numerators.
\frac{\left(x-2y\right)\left(y+x-2\right)}{xy}+1
Multiply \frac{x-2y}{x} times \frac{y+x-2}{y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-2y\right)\left(y+x-2\right)}{xy}+\frac{xy}{xy}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{xy}{xy}.
\frac{\left(x-2y\right)\left(y+x-2\right)+xy}{xy}
Since \frac{\left(x-2y\right)\left(y+x-2\right)}{xy} and \frac{xy}{xy} have the same denominator, add them by adding their numerators.
\frac{xy+x^{2}-2x-2y^{2}-2yx+4y+xy}{xy}
Do the multiplications in \left(x-2y\right)\left(y+x-2\right)+xy.
\frac{-2y^{2}+x^{2}-2x+4y}{xy}
Combine like terms in xy+x^{2}-2x-2y^{2}-2yx+4y+xy.
\frac{x-2y}{x}\left(\frac{y}{y}+\frac{x-2}{y}\right)+1
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{y}{y}.
\frac{x-2y}{x}\times \frac{y+x-2}{y}+1
Since \frac{y}{y} and \frac{x-2}{y} have the same denominator, add them by adding their numerators.
\frac{\left(x-2y\right)\left(y+x-2\right)}{xy}+1
Multiply \frac{x-2y}{x} times \frac{y+x-2}{y} by multiplying numerator times numerator and denominator times denominator.
\frac{\left(x-2y\right)\left(y+x-2\right)}{xy}+\frac{xy}{xy}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{xy}{xy}.
\frac{\left(x-2y\right)\left(y+x-2\right)+xy}{xy}
Since \frac{\left(x-2y\right)\left(y+x-2\right)}{xy} and \frac{xy}{xy} have the same denominator, add them by adding their numerators.
\frac{xy+x^{2}-2x-2y^{2}-2yx+4y+xy}{xy}
Do the multiplications in \left(x-2y\right)\left(y+x-2\right)+xy.
\frac{-2y^{2}+x^{2}-2x+4y}{xy}
Combine like terms in xy+x^{2}-2x-2y^{2}-2yx+4y+xy.
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}