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\frac{\frac{3}{x-1}-\frac{4\left(x-1\right)}{x-1}}{2-\frac{2}{x-1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x-1}{x-1}.
\frac{\frac{3-4\left(x-1\right)}{x-1}}{2-\frac{2}{x-1}}
Since \frac{3}{x-1} and \frac{4\left(x-1\right)}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3-4x+4}{x-1}}{2-\frac{2}{x-1}}
Do the multiplications in 3-4\left(x-1\right).
\frac{\frac{7-4x}{x-1}}{2-\frac{2}{x-1}}
Combine like terms in 3-4x+4.
\frac{\frac{7-4x}{x-1}}{\frac{2\left(x-1\right)}{x-1}-\frac{2}{x-1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-1}{x-1}.
\frac{\frac{7-4x}{x-1}}{\frac{2\left(x-1\right)-2}{x-1}}
Since \frac{2\left(x-1\right)}{x-1} and \frac{2}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{7-4x}{x-1}}{\frac{2x-2-2}{x-1}}
Do the multiplications in 2\left(x-1\right)-2.
\frac{\frac{7-4x}{x-1}}{\frac{2x-4}{x-1}}
Combine like terms in 2x-2-2.
\frac{\left(7-4x\right)\left(x-1\right)}{\left(x-1\right)\left(2x-4\right)}
Divide \frac{7-4x}{x-1} by \frac{2x-4}{x-1} by multiplying \frac{7-4x}{x-1} by the reciprocal of \frac{2x-4}{x-1}.
\frac{-4x+7}{2x-4}
Cancel out x-1 in both numerator and denominator.
\frac{\frac{3}{x-1}-\frac{4\left(x-1\right)}{x-1}}{2-\frac{2}{x-1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x-1}{x-1}.
\frac{\frac{3-4\left(x-1\right)}{x-1}}{2-\frac{2}{x-1}}
Since \frac{3}{x-1} and \frac{4\left(x-1\right)}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3-4x+4}{x-1}}{2-\frac{2}{x-1}}
Do the multiplications in 3-4\left(x-1\right).
\frac{\frac{7-4x}{x-1}}{2-\frac{2}{x-1}}
Combine like terms in 3-4x+4.
\frac{\frac{7-4x}{x-1}}{\frac{2\left(x-1\right)}{x-1}-\frac{2}{x-1}}
To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{x-1}{x-1}.
\frac{\frac{7-4x}{x-1}}{\frac{2\left(x-1\right)-2}{x-1}}
Since \frac{2\left(x-1\right)}{x-1} and \frac{2}{x-1} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{7-4x}{x-1}}{\frac{2x-2-2}{x-1}}
Do the multiplications in 2\left(x-1\right)-2.
\frac{\frac{7-4x}{x-1}}{\frac{2x-4}{x-1}}
Combine like terms in 2x-2-2.
\frac{\left(7-4x\right)\left(x-1\right)}{\left(x-1\right)\left(2x-4\right)}
Divide \frac{7-4x}{x-1} by \frac{2x-4}{x-1} by multiplying \frac{7-4x}{x-1} by the reciprocal of \frac{2x-4}{x-1}.
\frac{-4x+7}{2x-4}
Cancel out x-1 in both numerator and denominator.