Evaluate
\frac{x-3}{x+4}
Expand
\frac{x-3}{x+4}
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\frac{\left(\left(x-3\right)^{2}-4\right)\left(x^{2}-x-6\right)}{\left(\left(x+2\right)^{2}-7x-14\right)\left(\left(x+1\right)^{2}+x+1-6\right)}
Divide \frac{\left(x-3\right)^{2}-4}{\left(x+2\right)^{2}-7x-14} by \frac{\left(x+1\right)^{2}+x+1-6}{x^{2}-x-6} by multiplying \frac{\left(x-3\right)^{2}-4}{\left(x+2\right)^{2}-7x-14} by the reciprocal of \frac{\left(x+1\right)^{2}+x+1-6}{x^{2}-x-6}.
\frac{\left(\left(x-3\right)^{2}-4\right)\left(x^{2}-x-6\right)}{\left(\left(x+2\right)^{2}-7x-14\right)\left(\left(x+1\right)^{2}+x-5\right)}
Subtract 6 from 1 to get -5.
\frac{\left(x-5\right)\left(x-3\right)\left(x-1\right)\left(x+2\right)}{\left(x-5\right)\left(x-1\right)\left(x+2\right)\left(x+4\right)}
Factor the expressions that are not already factored.
\frac{x-3}{x+4}
Cancel out \left(x-5\right)\left(x-1\right)\left(x+2\right) in both numerator and denominator.
\frac{\left(\left(x-3\right)^{2}-4\right)\left(x^{2}-x-6\right)}{\left(\left(x+2\right)^{2}-7x-14\right)\left(\left(x+1\right)^{2}+x+1-6\right)}
Divide \frac{\left(x-3\right)^{2}-4}{\left(x+2\right)^{2}-7x-14} by \frac{\left(x+1\right)^{2}+x+1-6}{x^{2}-x-6} by multiplying \frac{\left(x-3\right)^{2}-4}{\left(x+2\right)^{2}-7x-14} by the reciprocal of \frac{\left(x+1\right)^{2}+x+1-6}{x^{2}-x-6}.
\frac{\left(\left(x-3\right)^{2}-4\right)\left(x^{2}-x-6\right)}{\left(\left(x+2\right)^{2}-7x-14\right)\left(\left(x+1\right)^{2}+x-5\right)}
Subtract 6 from 1 to get -5.
\frac{\left(x-5\right)\left(x-3\right)\left(x-1\right)\left(x+2\right)}{\left(x-5\right)\left(x-1\right)\left(x+2\right)\left(x+4\right)}
Factor the expressions that are not already factored.
\frac{x-3}{x+4}
Cancel out \left(x-5\right)\left(x-1\right)\left(x+2\right) in both numerator and denominator.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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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}