Evaluate
\frac{a-2}{a^{2}+a-8}
Expand
\frac{a-2}{a^{2}+a-8}
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\frac{a^{2}-4}{\left(a^{2}+a-8\right)\left(a^{2}-4\right)}\times \frac{a^{2}-4a+4}{a-2}
Express \frac{\frac{a^{2}-4}{a^{2}+a-8}}{a^{2}-4} as a single fraction.
\frac{1}{a^{2}+a-8}\times \frac{a^{2}-4a+4}{a-2}
Cancel out a^{2}-4 in both numerator and denominator.
\frac{1}{a^{2}+a-8}\times \frac{\left(a-2\right)^{2}}{a-2}
Factor the expressions that are not already factored in \frac{a^{2}-4a+4}{a-2}.
\frac{1}{a^{2}+a-8}\left(a-2\right)
Cancel out a-2 in both numerator and denominator.
\frac{a-2}{a^{2}+a-8}
Express \frac{1}{a^{2}+a-8}\left(a-2\right) as a single fraction.
\frac{a^{2}-4}{\left(a^{2}+a-8\right)\left(a^{2}-4\right)}\times \frac{a^{2}-4a+4}{a-2}
Express \frac{\frac{a^{2}-4}{a^{2}+a-8}}{a^{2}-4} as a single fraction.
\frac{1}{a^{2}+a-8}\times \frac{a^{2}-4a+4}{a-2}
Cancel out a^{2}-4 in both numerator and denominator.
\frac{1}{a^{2}+a-8}\times \frac{\left(a-2\right)^{2}}{a-2}
Factor the expressions that are not already factored in \frac{a^{2}-4a+4}{a-2}.
\frac{1}{a^{2}+a-8}\left(a-2\right)
Cancel out a-2 in both numerator and denominator.
\frac{a-2}{a^{2}+a-8}
Express \frac{1}{a^{2}+a-8}\left(a-2\right) as a single fraction.
Examples
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y = 3x + 4
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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}