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\frac{x^{2}}{x\left(x+2\right)}-\frac{x-2}{x+2}
Factor the expressions that are not already factored in \frac{x^{2}}{x^{2}+2x}.
\frac{x}{x+2}-\frac{x-2}{x+2}
Cancel out x in both numerator and denominator.
\frac{x-\left(x-2\right)}{x+2}
Since \frac{x}{x+2} and \frac{x-2}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{x-x+2}{x+2}
Do the multiplications in x-\left(x-2\right).
\frac{2}{x+2}
Combine like terms in x-x+2.
\frac{x^{2}}{x\left(x+2\right)}-\frac{x-2}{x+2}
Factor the expressions that are not already factored in \frac{x^{2}}{x^{2}+2x}.
\frac{x}{x+2}-\frac{x-2}{x+2}
Cancel out x in both numerator and denominator.
\frac{x-\left(x-2\right)}{x+2}
Since \frac{x}{x+2} and \frac{x-2}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{x-x+2}{x+2}
Do the multiplications in x-\left(x-2\right).
\frac{2}{x+2}
Combine like terms in x-x+2.