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\frac{\frac{x+2}{x+2}-\frac{x}{x+2}}{\frac{2}{x^{2}-4}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.
\frac{\frac{x+2-x}{x+2}}{\frac{2}{x^{2}-4}}
Since \frac{x+2}{x+2} and \frac{x}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{2}{x+2}}{\frac{2}{x^{2}-4}}
Combine like terms in x+2-x.
\frac{2\left(x^{2}-4\right)}{\left(x+2\right)\times 2}
Divide \frac{2}{x+2} by \frac{2}{x^{2}-4} by multiplying \frac{2}{x+2} by the reciprocal of \frac{2}{x^{2}-4}.
\frac{x^{2}-4}{x+2}
Cancel out 2 in both numerator and denominator.
\frac{\left(x-2\right)\left(x+2\right)}{x+2}
Factor the expressions that are not already factored.
x-2
Cancel out x+2 in both numerator and denominator.
\frac{\frac{x+2}{x+2}-\frac{x}{x+2}}{\frac{2}{x^{2}-4}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+2}{x+2}.
\frac{\frac{x+2-x}{x+2}}{\frac{2}{x^{2}-4}}
Since \frac{x+2}{x+2} and \frac{x}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{2}{x+2}}{\frac{2}{x^{2}-4}}
Combine like terms in x+2-x.
\frac{2\left(x^{2}-4\right)}{\left(x+2\right)\times 2}
Divide \frac{2}{x+2} by \frac{2}{x^{2}-4} by multiplying \frac{2}{x+2} by the reciprocal of \frac{2}{x^{2}-4}.
\frac{x^{2}-4}{x+2}
Cancel out 2 in both numerator and denominator.
\frac{\left(x-2\right)\left(x+2\right)}{x+2}
Factor the expressions that are not already factored.
x-2
Cancel out x+2 in both numerator and denominator.