Algebra Examples

$\frac{a}{c - 3} - \frac{6}{3 - c}$

Step 1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{a}{c - 3} - \frac{6}{- 1 (- 3) - c}$

Step 2

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

$\frac{a}{c - 3} - \frac{6}{- 1 (- 3) - (c)}$

Step 3

Factor $- 1$ out of $- 1 (- 3) - (c)$ .

$\frac{a}{c - 3} - \frac{6}{- 1 (- 3 + c)}$

Step 4

Reorder terms.

$\frac{a}{c - 3} - \frac{6}{- 1 (c - 3)}$

Step 5

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

$\frac{a}{c - 3} \cdot \frac{- 1}{- 1} - \frac{6}{- 1 (c - 3)}$

Step 6

Write each expression with a common denominator of $(c - 3) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{a}{c - 3}$ by $\frac{- 1}{- 1}$ .

$\frac{a \cdot - 1}{(c - 3) \cdot - 1} - \frac{6}{- 1 (c - 3)}$

Step 6.2

Reorder the factors of $(c - 3) \cdot - 1$ .

$\frac{a \cdot - 1}{- (c - 3)} - \frac{6}{- 1 (c - 3)}$

Step 7

Combine the numerators over the common denominator.

$\frac{a \cdot - 1 - 6}{- (c - 3)}$

Step 8

Simplify the numerator.

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Step 8.1

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

$\frac{- 1 \cdot a - 6}{- (c - 3)}$

Step 8.2

Rewrite $- 1 a$ as $- a$ .

$\frac{- a - 6}{- (c - 3)}$

Step 9

Simplify with factoring out.

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Step 9.1

Move the negative in front of the fraction.

$- \frac{- a - 6}{c - 3}$

Step 9.2

Factor $- 1$ out of $- a$ .

$- \frac{- (a) - 6}{c - 3}$

Step 9.3

Rewrite $- 6$ as $- 1 (6)$ .

$- \frac{- (a) - 1 (6)}{c - 3}$

Step 9.4

Factor $- 1$ out of $- (a) - 1 (6)$ .

$- \frac{- (a + 6)}{c - 3}$

Step 9.5

Simplify the expression.

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Step 9.5.1

Rewrite $- (a + 6)$ as $- 1 (a + 6)$ .

$- \frac{- 1 (a + 6)}{c - 3}$

Step 9.5.2

Move the negative in front of the fraction.

$- - \frac{a + 6}{c - 3}$

Step 9.5.3

Multiply $- 1$ by $- 1$ .

$1 \frac{a + 6}{c - 3}$

Step 9.5.4

Multiply $\frac{a + 6}{c - 3}$ by $1$ .

$\frac{a + 6}{c - 3}$