Evaluate (3/(x-1)-4)/(2-2/(x-1))

$\frac{\frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1}}$

Multiply the numerator and denominator of the complex fraction by $x - 1$ .

Multiply $\frac{\frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1}}$ by $\frac{x - 1}{x - 1}$ .

$\frac{x - 1}{x - 1} \cdot \frac{\frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1}}$

Combine.

$\frac{(x - 1) (\frac{3}{x - 1} - 4)}{(x - 1) (2 - \frac{2}{x - 1})}$

Apply the distributive property.

$\frac{(x - 1) \frac{3}{x - 1} + (x - 1) \cdot - 4}{(x - 1) \cdot 2 + (x - 1) (- \frac{2}{x - 1})}$

Simplify by cancelling.

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{(x - 1) \frac{3}{x - 1} + (x - 1) \cdot - 4}{(x - 1) \cdot 2 + (x - 1) (- \frac{2}{x - 1})}$

Rewrite the expression.

$\frac{3 + (x - 1) \cdot - 4}{(x - 1) \cdot 2 + (x - 1) (- \frac{2}{x - 1})}$

Cancel the common factor of $x - 1$ .

Move the leading negative in $- \frac{2}{x - 1}$ into the numerator.

$\frac{3 + (x - 1) \cdot - 4}{(x - 1) \cdot 2 + (x - 1) \frac{- 2}{x - 1}}$

Cancel the common factor.

$\frac{3 + (x - 1) \cdot - 4}{(x - 1) \cdot 2 + (x - 1) \frac{- 2}{x - 1}}$

Rewrite the expression.

$\frac{3 + (x - 1) \cdot - 4}{(x - 1) \cdot 2 - 2}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 + x \cdot - 4 - 1 \cdot - 4}{(x - 1) \cdot 2 - 2}$

Move $- 4$ to the left of $x$ .

$\frac{3 - 4 \cdot x - 1 \cdot - 4}{(x - 1) \cdot 2 - 2}$

Multiply $- 1$ by $- 4$ .

$\frac{3 - 4 \cdot x + 4}{(x - 1) \cdot 2 - 2}$

Add $3$ and $4$ .

$\frac{- 4 x + 7}{(x - 1) \cdot 2 - 2}$

Simplify the denominator.

Factor $2$ out of $(x - 1) \cdot 2 - 2$ .

Factor $2$ out of $(x - 1) \cdot 2$ .

$\frac{- 4 x + 7}{2 \cdot (x - 1) - 2}$

Factor $2$ out of $- 2$ .

$\frac{- 4 x + 7}{2 \cdot (x - 1) + 2 (- 1)}$

Factor $2$ out of $2 \cdot (x - 1) + 2 (- 1)$ .

$\frac{- 4 x + 7}{2 (x - 1 - 1)}$

Subtract $1$ from $- 1$ .

$\frac{- 4 x + 7}{2 (x - 2)}$

Simplify with factoring out.

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) + 7}{2 (x - 2)}$

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{- (4 x) - 1 (- 7)}{2 (x - 2)}$

Factor $- 1$ out of $- (4 x) - 1 (- 7)$ .

$\frac{- (4 x - 7)}{2 (x - 2)}$

Simplify the expression.

Rewrite $- (4 x - 7)$ as $- 1 (4 x - 7)$ .

$\frac{- 1 (4 x - 7)}{2 (x - 2)}$

Move the negative in front of the fraction.

$- \frac{4 x - 7}{2 (x - 2)}$

Evaluate (3/(x-1)-4)/(2-2/(x-1))

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