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\frac{y}{x}
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\frac{y}{x}
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\frac{y\left(y-1\right)}{x\left(y-1\right)}+\frac{xy^{2}}{x^{2}y}-\frac{xy+2y}{x^{2}+2x}
Factor the expressions that are not already factored in \frac{y^{2}-y}{xy-x}.
\frac{y}{x}+\frac{xy^{2}}{x^{2}y}-\frac{xy+2y}{x^{2}+2x}
Cancel out y-1 in both numerator and denominator.
\frac{y}{x}+\frac{y}{x}-\frac{xy+2y}{x^{2}+2x}
Cancel out xy in both numerator and denominator.
2\times \frac{y}{x}-\frac{xy+2y}{x^{2}+2x}
Combine \frac{y}{x} and \frac{y}{x} to get 2\times \frac{y}{x}.
2\times \frac{y}{x}-\frac{y\left(x+2\right)}{x\left(x+2\right)}
Factor the expressions that are not already factored in \frac{xy+2y}{x^{2}+2x}.
2\times \frac{y}{x}-\frac{y}{x}
Cancel out x+2 in both numerator and denominator.
\frac{2y}{x}-\frac{y}{x}
Express 2\times \frac{y}{x} as a single fraction.
\frac{2y-y}{x}
Since \frac{2y}{x} and \frac{y}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{y}{x}
Combine like terms in 2y-y.
\frac{y\left(y-1\right)}{x\left(y-1\right)}+\frac{xy^{2}}{x^{2}y}-\frac{xy+2y}{x^{2}+2x}
Factor the expressions that are not already factored in \frac{y^{2}-y}{xy-x}.
\frac{y}{x}+\frac{xy^{2}}{x^{2}y}-\frac{xy+2y}{x^{2}+2x}
Cancel out y-1 in both numerator and denominator.
\frac{y}{x}+\frac{y}{x}-\frac{xy+2y}{x^{2}+2x}
Cancel out xy in both numerator and denominator.
2\times \frac{y}{x}-\frac{xy+2y}{x^{2}+2x}
Combine \frac{y}{x} and \frac{y}{x} to get 2\times \frac{y}{x}.
2\times \frac{y}{x}-\frac{y\left(x+2\right)}{x\left(x+2\right)}
Factor the expressions that are not already factored in \frac{xy+2y}{x^{2}+2x}.
2\times \frac{y}{x}-\frac{y}{x}
Cancel out x+2 in both numerator and denominator.
\frac{2y}{x}-\frac{y}{x}
Express 2\times \frac{y}{x} as a single fraction.
\frac{2y-y}{x}
Since \frac{2y}{x} and \frac{y}{x} have the same denominator, subtract them by subtracting their numerators.
\frac{y}{x}
Combine like terms in 2y-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}