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\frac{x\left(x+1\right)+x\left(1-x\right)}{x-2}
Since \frac{x\left(x+1\right)}{x-2} and \frac{x\left(1-x\right)}{x-2} have the same denominator, add them by adding their numerators.
\frac{x^{2}+x+x-x^{2}}{x-2}
Do the multiplications in x\left(x+1\right)+x\left(1-x\right).
\frac{2x}{x-2}
Combine like terms in x^{2}+x+x-x^{2}.
\frac{x\left(x+1\right)+x\left(1-x\right)}{x-2}
Since \frac{x\left(x+1\right)}{x-2} and \frac{x\left(1-x\right)}{x-2} have the same denominator, add them by adding their numerators.
\frac{x^{2}+x+x-x^{2}}{x-2}
Do the multiplications in x\left(x+1\right)+x\left(1-x\right).
\frac{2x}{x-2}
Combine like terms in x^{2}+x+x-x^{2}.