Simplify (3x+2)/(4x-5)-(x-1)/(5-4x)

$\frac{3 x + 2}{4 x - 5} - \frac{x - 1}{5 - 4 x}$

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{3 x + 2}{4 x - 5} - \frac{x - 1}{- 1 (- 5) - 4 x}$

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

$\frac{3 x + 2}{4 x - 5} - \frac{x - 1}{- 1 (- 5) - (4 x)}$

Factor $- 1$ out of $- 1 (- 5) - (4 x)$ .

$\frac{3 x + 2}{4 x - 5} - \frac{x - 1}{- 1 (- 5 + 4 x)}$

Reorder terms.

$\frac{3 x + 2}{4 x - 5} - \frac{x - 1}{- 1 (4 x - 5)}$

To write $\frac{3 x + 2}{4 x - 5}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{3 x + 2}{4 x - 5} \cdot \frac{- 1}{- 1} - \frac{x - 1}{- 1 (4 x - 5)}$

Write each expression with a common denominator of $(4 x - 5) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x + 2}{4 x - 5}$ by $\frac{- 1}{- 1}$ .

$\frac{(3 x + 2) \cdot - 1}{(4 x - 5) \cdot - 1} - \frac{x - 1}{- 1 (4 x - 5)}$

Reorder the factors of $(4 x - 5) \cdot - 1$ .

$\frac{(3 x + 2) \cdot - 1}{- (4 x - 5)} - \frac{x - 1}{- 1 (4 x - 5)}$

Combine the numerators over the common denominator.

$\frac{(3 x + 2) \cdot - 1 - (x - 1)}{- (4 x - 5)}$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot - 1 + 2 \cdot - 1 - (x - 1)}{- (4 x - 5)}$

Multiply $- 1$ by $3$ .

$\frac{- 3 x + 2 \cdot - 1 - (x - 1)}{- (4 x - 5)}$

Multiply $2$ by $- 1$ .

$\frac{- 3 x - 2 - (x - 1)}{- (4 x - 5)}$

Apply the distributive property.

$\frac{- 3 x - 2 - x - - 1}{- (4 x - 5)}$

Multiply $- 1$ by $- 1$ .

$\frac{- 3 x - 2 - x + 1}{- (4 x - 5)}$

Subtract $x$ from $- 3 x$ .

$\frac{- 4 x - 2 + 1}{- (4 x - 5)}$

Add $- 2$ and $1$ .

$\frac{- 4 x - 1}{- (4 x - 5)}$

Simplify with factoring out.

Move the negative in front of the fraction.

$- \frac{- 4 x - 1}{4 x - 5}$

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

$- \frac{- (4 x) - 1}{4 x - 5}$

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

$- \frac{- (4 x) - 1 (1)}{4 x - 5}$

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

$- \frac{- (4 x + 1)}{4 x - 5}$

Simplify the expression.

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

$- \frac{- 1 (4 x + 1)}{4 x - 5}$

Move the negative in front of the fraction.

$- - \frac{4 x + 1}{4 x - 5}$

Multiply $- 1$ by $- 1$ .

$1 \frac{4 x + 1}{4 x - 5}$

Multiply $\frac{4 x + 1}{4 x - 5}$ by $1$ .

$\frac{4 x + 1}{4 x - 5}$

Simplify (3x+2)/(4x-5)-(x-1)/(5-4x)

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