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\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}-\left(x-2\right)}
Anything divided by one gives itself.
\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}-x-\left(-2\right)}
To find the opposite of x-2, find the opposite of each term.
\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}-x+2}
The opposite of -2 is 2.
\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}+\frac{\left(-x+2\right)\left(x-2\right)}{x-2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply -x+2 times \frac{x-2}{x-2}.
\frac{\frac{3-x}{x-2}}{\frac{5+\left(-x+2\right)\left(x-2\right)}{x-2}}
Since \frac{5}{x-2} and \frac{\left(-x+2\right)\left(x-2\right)}{x-2} have the same denominator, add them by adding their numerators.
\frac{\frac{3-x}{x-2}}{\frac{5-x^{2}+2x+2x-4}{x-2}}
Do the multiplications in 5+\left(-x+2\right)\left(x-2\right).
\frac{\frac{3-x}{x-2}}{\frac{1-x^{2}+4x}{x-2}}
Combine like terms in 5-x^{2}+2x+2x-4.
\frac{\left(3-x\right)\left(x-2\right)}{\left(x-2\right)\left(1-x^{2}+4x\right)}
Divide \frac{3-x}{x-2} by \frac{1-x^{2}+4x}{x-2} by multiplying \frac{3-x}{x-2} by the reciprocal of \frac{1-x^{2}+4x}{x-2}.
\frac{-x+3}{-x^{2}+4x+1}
Cancel out x-2 in both numerator and denominator.
\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}-\left(x-2\right)}
Anything divided by one gives itself.
\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}-x-\left(-2\right)}
To find the opposite of x-2, find the opposite of each term.
\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}-x+2}
The opposite of -2 is 2.
\frac{\frac{3-x}{x-2}}{\frac{5}{x-2}+\frac{\left(-x+2\right)\left(x-2\right)}{x-2}}
To add or subtract expressions, expand them to make their denominators the same. Multiply -x+2 times \frac{x-2}{x-2}.
\frac{\frac{3-x}{x-2}}{\frac{5+\left(-x+2\right)\left(x-2\right)}{x-2}}
Since \frac{5}{x-2} and \frac{\left(-x+2\right)\left(x-2\right)}{x-2} have the same denominator, add them by adding their numerators.
\frac{\frac{3-x}{x-2}}{\frac{5-x^{2}+2x+2x-4}{x-2}}
Do the multiplications in 5+\left(-x+2\right)\left(x-2\right).
\frac{\frac{3-x}{x-2}}{\frac{1-x^{2}+4x}{x-2}}
Combine like terms in 5-x^{2}+2x+2x-4.
\frac{\left(3-x\right)\left(x-2\right)}{\left(x-2\right)\left(1-x^{2}+4x\right)}
Divide \frac{3-x}{x-2} by \frac{1-x^{2}+4x}{x-2} by multiplying \frac{3-x}{x-2} by the reciprocal of \frac{1-x^{2}+4x}{x-2}.
\frac{-x+3}{-x^{2}+4x+1}
Cancel out x-2 in both numerator and denominator.