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\frac{\frac{4}{\left(x-2\right)\left(x+2\right)}+\frac{1}{x+2}}{\frac{1}{x-2}}
Factor x^{2}-4.
\frac{\frac{4}{\left(x-2\right)\left(x+2\right)}+\frac{x-2}{\left(x-2\right)\left(x+2\right)}}{\frac{1}{x-2}}
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 x+2 is \left(x-2\right)\left(x+2\right). Multiply \frac{1}{x+2} times \frac{x-2}{x-2}.
\frac{\frac{4+x-2}{\left(x-2\right)\left(x+2\right)}}{\frac{1}{x-2}}
Since \frac{4}{\left(x-2\right)\left(x+2\right)} and \frac{x-2}{\left(x-2\right)\left(x+2\right)} have the same denominator, add them by adding their numerators.
\frac{\frac{2+x}{\left(x-2\right)\left(x+2\right)}}{\frac{1}{x-2}}
Combine like terms in 4+x-2.
\frac{\frac{1}{x-2}}{\frac{1}{x-2}}
Cancel out x+2 in both numerator and denominator.
\frac{x-2}{x-2}
Divide \frac{1}{x-2} by \frac{1}{x-2} by multiplying \frac{1}{x-2} by the reciprocal of \frac{1}{x-2}.
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Cancel out x-2 in both numerator and denominator.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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}