Evaluate
\frac{2\left(x-36\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
Expand
\frac{2\left(x-36\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
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\frac{9\left(x-1\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}-\frac{7\left(x+9\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+9\right)\left(x+3\right) and \left(x+3\right)\left(x-1\right) is \left(x-1\right)\left(x+3\right)\left(x+9\right). Multiply \frac{9}{\left(x+9\right)\left(x+3\right)} times \frac{x-1}{x-1}. Multiply \frac{7}{\left(x+3\right)\left(x-1\right)} times \frac{x+9}{x+9}.
\frac{9\left(x-1\right)-7\left(x+9\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
Since \frac{9\left(x-1\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)} and \frac{7\left(x+9\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{9x-9-7x-63}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
Do the multiplications in 9\left(x-1\right)-7\left(x+9\right).
\frac{2x-72}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
Combine like terms in 9x-9-7x-63.
\frac{2x-72}{x^{3}+11x^{2}+15x-27}
Expand \left(x-1\right)\left(x+3\right)\left(x+9\right).
\frac{9\left(x-1\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}-\frac{7\left(x+9\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+9\right)\left(x+3\right) and \left(x+3\right)\left(x-1\right) is \left(x-1\right)\left(x+3\right)\left(x+9\right). Multiply \frac{9}{\left(x+9\right)\left(x+3\right)} times \frac{x-1}{x-1}. Multiply \frac{7}{\left(x+3\right)\left(x-1\right)} times \frac{x+9}{x+9}.
\frac{9\left(x-1\right)-7\left(x+9\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
Since \frac{9\left(x-1\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)} and \frac{7\left(x+9\right)}{\left(x-1\right)\left(x+3\right)\left(x+9\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{9x-9-7x-63}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
Do the multiplications in 9\left(x-1\right)-7\left(x+9\right).
\frac{2x-72}{\left(x-1\right)\left(x+3\right)\left(x+9\right)}
Combine like terms in 9x-9-7x-63.
\frac{2x-72}{x^{3}+11x^{2}+15x-27}
Expand \left(x-1\right)\left(x+3\right)\left(x+9\right).
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}