Evaluate
\frac{8}{x^{2}-4}
Factor
\frac{8}{x^{2}-4}
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\frac{4x}{\left(x-2\right)\left(x+2\right)}-\frac{4}{2+x}
Factor x^{2}-4.
\frac{4x}{\left(x-2\right)\left(x+2\right)}-\frac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-2\right)\left(x+2\right) and 2+x is \left(x-2\right)\left(x+2\right). Multiply \frac{4}{2+x} times \frac{x-2}{x-2}.
\frac{4x-4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}
Since \frac{4x}{\left(x-2\right)\left(x+2\right)} and \frac{4\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x-4x+8}{\left(x-2\right)\left(x+2\right)}
Do the multiplications in 4x-4\left(x-2\right).
\frac{8}{\left(x-2\right)\left(x+2\right)}
Combine like terms in 4x-4x+8.
\frac{8}{x^{2}-4}
Expand \left(x-2\right)\left(x+2\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
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Limits
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