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\frac{1}{x-2}
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\frac{x\left(x+2\right)}{\left(x^{2}+6x+8\right)\left(x-2\right)}+\frac{4}{x^{2}+2x-8}
Divide \frac{x}{x^{2}+6x+8} by \frac{x-2}{x+2} by multiplying \frac{x}{x^{2}+6x+8} by the reciprocal of \frac{x-2}{x+2}.
\frac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(x+4\right)}+\frac{4}{x^{2}+2x-8}
Factor the expressions that are not already factored in \frac{x\left(x+2\right)}{\left(x^{2}+6x+8\right)\left(x-2\right)}.
\frac{x}{\left(x-2\right)\left(x+4\right)}+\frac{4}{x^{2}+2x-8}
Cancel out x+2 in both numerator and denominator.
\frac{x}{\left(x-2\right)\left(x+4\right)}+\frac{4}{\left(x-2\right)\left(x+4\right)}
Factor x^{2}+2x-8.
\frac{x+4}{\left(x-2\right)\left(x+4\right)}
Since \frac{x}{\left(x-2\right)\left(x+4\right)} and \frac{4}{\left(x-2\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{1}{x-2}
Cancel out x+4 in both numerator and denominator.
\frac{x\left(x+2\right)}{\left(x^{2}+6x+8\right)\left(x-2\right)}+\frac{4}{x^{2}+2x-8}
Divide \frac{x}{x^{2}+6x+8} by \frac{x-2}{x+2} by multiplying \frac{x}{x^{2}+6x+8} by the reciprocal of \frac{x-2}{x+2}.
\frac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)\left(x+4\right)}+\frac{4}{x^{2}+2x-8}
Factor the expressions that are not already factored in \frac{x\left(x+2\right)}{\left(x^{2}+6x+8\right)\left(x-2\right)}.
\frac{x}{\left(x-2\right)\left(x+4\right)}+\frac{4}{x^{2}+2x-8}
Cancel out x+2 in both numerator and denominator.
\frac{x}{\left(x-2\right)\left(x+4\right)}+\frac{4}{\left(x-2\right)\left(x+4\right)}
Factor x^{2}+2x-8.
\frac{x+4}{\left(x-2\right)\left(x+4\right)}
Since \frac{x}{\left(x-2\right)\left(x+4\right)} and \frac{4}{\left(x-2\right)\left(x+4\right)} have the same denominator, add them by adding their numerators.
\frac{1}{x-2}
Cancel out x+4 in both numerator and denominator.
Examples
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y = 3x + 4
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Matrix
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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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