Evaluate
-\frac{1}{x-2}
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-\frac{1}{x-2}
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\frac{2x-6+3-3x}{x^{2}+x-6}
Since \frac{2x-6}{x^{2}+x-6} and \frac{3-3x}{x^{2}+x-6} have the same denominator, add them by adding their numerators.
\frac{-x-3}{x^{2}+x-6}
Combine like terms in 2x-6+3-3x.
\frac{-x-3}{\left(x-2\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{-x-3}{x^{2}+x-6}.
\frac{-\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}
Extract the negative sign in -3-x.
\frac{-1}{x-2}
Cancel out x+3 in both numerator and denominator.
\frac{2x-6+3-3x}{x^{2}+x-6}
Since \frac{2x-6}{x^{2}+x-6} and \frac{3-3x}{x^{2}+x-6} have the same denominator, add them by adding their numerators.
\frac{-x-3}{x^{2}+x-6}
Combine like terms in 2x-6+3-3x.
\frac{-x-3}{\left(x-2\right)\left(x+3\right)}
Factor the expressions that are not already factored in \frac{-x-3}{x^{2}+x-6}.
\frac{-\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}
Extract the negative sign in -3-x.
\frac{-1}{x-2}
Cancel out x+3 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}