Evaluate
\frac{x}{1-x}
Expand
-\frac{x}{x-1}
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\frac{\left(3x-2\right)\left(3x+2\right)}{\left(3x-2\right)\left(-x+1\right)}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8x}
Factor the expressions that are not already factored in \frac{9x^{2}-4}{-3x^{2}+5x-2}.
\frac{3x+2}{-x+1}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8x}
Cancel out 3x-2 in both numerator and denominator.
\frac{3x+2}{-x+1}\times \frac{x^{2}\left(9x^{2}-6x+4\right)}{x\left(3x+2\right)\left(9x^{2}-6x+4\right)}
Factor the expressions that are not already factored in \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8x}.
\frac{3x+2}{-x+1}\times \frac{x}{3x+2}
Cancel out x\left(9x^{2}-6x+4\right) in both numerator and denominator.
\frac{\left(3x+2\right)x}{\left(-x+1\right)\left(3x+2\right)}
Multiply \frac{3x+2}{-x+1} times \frac{x}{3x+2} by multiplying numerator times numerator and denominator times denominator.
\frac{x}{-x+1}
Cancel out 3x+2 in both numerator and denominator.
\frac{\left(3x-2\right)\left(3x+2\right)}{\left(3x-2\right)\left(-x+1\right)}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8x}
Factor the expressions that are not already factored in \frac{9x^{2}-4}{-3x^{2}+5x-2}.
\frac{3x+2}{-x+1}\times \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8x}
Cancel out 3x-2 in both numerator and denominator.
\frac{3x+2}{-x+1}\times \frac{x^{2}\left(9x^{2}-6x+4\right)}{x\left(3x+2\right)\left(9x^{2}-6x+4\right)}
Factor the expressions that are not already factored in \frac{9x^{4}-6x^{3}+4x^{2}}{27x^{4}+8x}.
\frac{3x+2}{-x+1}\times \frac{x}{3x+2}
Cancel out x\left(9x^{2}-6x+4\right) in both numerator and denominator.
\frac{\left(3x+2\right)x}{\left(-x+1\right)\left(3x+2\right)}
Multiply \frac{3x+2}{-x+1} times \frac{x}{3x+2} by multiplying numerator times numerator and denominator times denominator.
\frac{x}{-x+1}
Cancel out 3x+2 in both numerator and denominator.
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}