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\frac{x+2}{x+7}
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\frac{x+2}{x+7}
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\frac{x^{2}-9x-\left(4-9x\right)}{x^{2}+5x-14}
Since \frac{x^{2}-9x}{x^{2}+5x-14} and \frac{4-9x}{x^{2}+5x-14} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-9x-4+9x}{x^{2}+5x-14}
Do the multiplications in x^{2}-9x-\left(4-9x\right).
\frac{x^{2}-4}{x^{2}+5x-14}
Combine like terms in x^{2}-9x-4+9x.
\frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+7\right)}
Factor the expressions that are not already factored in \frac{x^{2}-4}{x^{2}+5x-14}.
\frac{x+2}{x+7}
Cancel out x-2 in both numerator and denominator.
\frac{x^{2}-9x-\left(4-9x\right)}{x^{2}+5x-14}
Since \frac{x^{2}-9x}{x^{2}+5x-14} and \frac{4-9x}{x^{2}+5x-14} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}-9x-4+9x}{x^{2}+5x-14}
Do the multiplications in x^{2}-9x-\left(4-9x\right).
\frac{x^{2}-4}{x^{2}+5x-14}
Combine like terms in x^{2}-9x-4+9x.
\frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+7\right)}
Factor the expressions that are not already factored in \frac{x^{2}-4}{x^{2}+5x-14}.
\frac{x+2}{x+7}
Cancel out x-2 in both numerator and denominator.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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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}