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