Simplify (x-3)/(x-1)-2/(1-x)

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

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

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

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

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

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

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

Reorder terms.

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

To write $\frac{x - 3}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

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

Write each expression with a common denominator of $(x - 1) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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

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

Reorder the factors of $(x - 1) \cdot - 1$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Move $- 1$ to the left of $x$ .

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

Multiply $- 3$ by $- 1$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Subtract $2$ from $3$ .

$\frac{- x + 1}{- (x - 1)}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- x + 1$ and $x - 1$ .

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

$\frac{- (x) + 1}{- (x - 1)}$

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

$\frac{- (x) - 1 (- 1)}{- (x - 1)}$

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

$\frac{- (x - 1)}{- (x - 1)}$

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

$\frac{- 1 (x - 1)}{- (x - 1)}$

Cancel the common factor.

$\frac{- 1 (x - 1)}{- (x - 1)}$

Rewrite the expression.

$\frac{- 1}{- 1}$

Move the negative one from the denominator of $\frac{- 1}{- 1}$ .

$- 1 \cdot - 1$

Simplify the expression.

Rewrite $- 1 \cdot - 1$ as $- - 1$ .

$- - 1$

Multiply $- 1$ by $- 1$ .

$1$

Simplify (x-3)/(x-1)-2/(1-x)

Related Questions

Support LCMGCF.com by disabling your adblocker.