Simplify v/(v-c)-c/(c-v)

$\frac{v}{v - c} - \frac{c}{c - v}$

Step 1

Factor $- 1$ out of $c$ .

$\frac{v}{v - c} - \frac{c}{- 1 (- c) - v}$

Step 2

Factor $- 1$ out of $- v$ .

$\frac{v}{v - c} - \frac{c}{- 1 (- c) - (v)}$

Step 3

Factor $- 1$ out of $- 1 (- c) - (v)$ .

$\frac{v}{v - c} - \frac{c}{- 1 (- c + v)}$

Step 4

Reorder terms.

$\frac{v}{- c + v} - \frac{c}{- 1 (- c + v)}$

Step 5

To write $\frac{v}{- c + v}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{v}{- c + v} \cdot \frac{- 1}{- 1} - \frac{c}{- 1 (- c + v)}$

Step 6

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

Multiply $\frac{v}{- c + v}$ by $\frac{- 1}{- 1}$ .

$\frac{v \cdot - 1}{(- c + v) \cdot - 1} - \frac{c}{- 1 (- c + v)}$

Reorder the factors of $(- c + v) \cdot - 1$ .

$\frac{v \cdot - 1}{- (- c + v)} - \frac{c}{- 1 (- c + v)}$

Step 7

Combine the numerators over the common denominator.

$\frac{v \cdot - 1 - c}{- (- c + v)}$

Step 8

Simplify the numerator.

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

$\frac{- 1 \cdot v - c}{- (- c + v)}$

Rewrite $- 1 v$ as $- v$ .

$\frac{- v - c}{- (- c + v)}$

Step 9

Simplify terms.

Move the negative in front of the fraction.

$- \frac{- v - c}{- c + v}$

Factor $- 1$ out of $- v$ .

$- \frac{- (v) - c}{- c + v}$

Factor $- 1$ out of $- c$ .

$- \frac{- (v) - (c)}{- c + v}$

Factor $- 1$ out of $- (v) - (c)$ .

$- \frac{- (v + c)}{- c + v}$

Rewrite $- (v + c)$ as $- 1 (v + c)$ .

$- \frac{- 1 (v + c)}{- c + v}$

Factor $- 1$ out of $- c$ .

$- \frac{- 1 (v + c)}{- (c) + v}$

Factor $- 1$ out of $v$ .

$- \frac{- 1 (v + c)}{- (c) - 1 (- v)}$

Factor $- 1$ out of $- (c) - 1 (- v)$ .

$- \frac{- 1 (v + c)}{- (c - v)}$

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

$- \frac{- 1 (v + c)}{- 1 (c - v)}$

Cancel the common factor.

$- \frac{- 1 (v + c)}{- 1 (c - v)}$

Rewrite the expression.

$- \frac{v + c}{c - v}$

Simplify v/(v-c)-c/(c-v)

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