Evaluate
-\frac{\left(x-11\right)\left(x+3\right)}{8\left(1-x^{2}\right)}
Factor
-\frac{\left(x-11\right)\left(x+3\right)}{8\left(1-x^{2}\right)}
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\frac{1}{8}-\frac{3}{\left(x-1\right)\left(x+1\right)}+\frac{1}{1-x}
Factor x^{2}-1.
\frac{\left(x-1\right)\left(x+1\right)}{8\left(x-1\right)\left(x+1\right)}-\frac{3\times 8}{8\left(x-1\right)\left(x+1\right)}+\frac{1}{1-x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and \left(x-1\right)\left(x+1\right) is 8\left(x-1\right)\left(x+1\right). Multiply \frac{1}{8} times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}. Multiply \frac{3}{\left(x-1\right)\left(x+1\right)} times \frac{8}{8}.
\frac{\left(x-1\right)\left(x+1\right)-3\times 8}{8\left(x-1\right)\left(x+1\right)}+\frac{1}{1-x}
Since \frac{\left(x-1\right)\left(x+1\right)}{8\left(x-1\right)\left(x+1\right)} and \frac{3\times 8}{8\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{2}+x-x-1-24}{8\left(x-1\right)\left(x+1\right)}+\frac{1}{1-x}
Do the multiplications in \left(x-1\right)\left(x+1\right)-3\times 8.
\frac{x^{2}-25}{8\left(x-1\right)\left(x+1\right)}+\frac{1}{1-x}
Combine like terms in x^{2}+x-x-1-24.
\frac{x^{2}-25}{8\left(x-1\right)\left(x+1\right)}+\frac{-8\left(x+1\right)}{8\left(x-1\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8\left(x-1\right)\left(x+1\right) and 1-x is 8\left(x-1\right)\left(x+1\right). Multiply \frac{1}{1-x} times \frac{-8\left(x+1\right)}{-8\left(x+1\right)}.
\frac{x^{2}-25-8\left(x+1\right)}{8\left(x-1\right)\left(x+1\right)}
Since \frac{x^{2}-25}{8\left(x-1\right)\left(x+1\right)} and \frac{-8\left(x+1\right)}{8\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}-25-8x-8}{8\left(x-1\right)\left(x+1\right)}
Do the multiplications in x^{2}-25-8\left(x+1\right).
\frac{x^{2}-33-8x}{8\left(x-1\right)\left(x+1\right)}
Combine like terms in x^{2}-25-8x-8.
\frac{x^{2}-33-8x}{8x^{2}-8}
Expand 8\left(x-1\right)\left(x+1\right).
Examples
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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
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