Evaluate
\frac{x-8}{x+9}
Expand
\frac{x-8}{x+9}
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\frac{3x^{2}-3x-72-\left(2x^{2}-4x\right)}{x^{2}+18x+81}
Since \frac{3x^{2}-3x-72}{x^{2}+18x+81} and \frac{2x^{2}-4x}{x^{2}+18x+81} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-3x-72-2x^{2}+4x}{x^{2}+18x+81}
Do the multiplications in 3x^{2}-3x-72-\left(2x^{2}-4x\right).
\frac{x^{2}+x-72}{x^{2}+18x+81}
Combine like terms in 3x^{2}-3x-72-2x^{2}+4x.
\frac{\left(x-8\right)\left(x+9\right)}{\left(x+9\right)^{2}}
Factor the expressions that are not already factored in \frac{x^{2}+x-72}{x^{2}+18x+81}.
\frac{x-8}{x+9}
Cancel out x+9 in both numerator and denominator.
\frac{3x^{2}-3x-72-\left(2x^{2}-4x\right)}{x^{2}+18x+81}
Since \frac{3x^{2}-3x-72}{x^{2}+18x+81} and \frac{2x^{2}-4x}{x^{2}+18x+81} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}-3x-72-2x^{2}+4x}{x^{2}+18x+81}
Do the multiplications in 3x^{2}-3x-72-\left(2x^{2}-4x\right).
\frac{x^{2}+x-72}{x^{2}+18x+81}
Combine like terms in 3x^{2}-3x-72-2x^{2}+4x.
\frac{\left(x-8\right)\left(x+9\right)}{\left(x+9\right)^{2}}
Factor the expressions that are not already factored in \frac{x^{2}+x-72}{x^{2}+18x+81}.
\frac{x-8}{x+9}
Cancel out x+9 in both numerator and denominator.
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Simultaneous equation
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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}