Basic Math Examples

$\frac{4 c - 6}{3 c - 2} + \frac{2 c - 8}{2 - 3 c} + \frac{2 - 3 c}{- 2 + 3 c}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{4 c - 6 + 2 - 3 c}{3 c - 2} + \frac{2 c - 8}{- 3 c + 2}$

Step 1.2

Subtract $3 c$ from $4 c$ .

$\frac{c - 6 + 2}{3 c - 2} + \frac{2 c - 8}{- 3 c + 2}$

Step 1.3

Add $- 6$ and $2$ .

$\frac{c - 4}{3 c - 2} + \frac{2 c - 8}{- 3 c + 2}$

Step 1.4

Factor $2$ out of $2 c - 8$ .

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Step 1.4.1

Factor $2$ out of $2 c$ .

$\frac{c - 4}{3 c - 2} + \frac{2 (c) - 8}{- 3 c + 2}$

Step 1.4.2

Factor $2$ out of $- 8$ .

$\frac{c - 4}{3 c - 2} + \frac{2 c + 2 \cdot - 4}{- 3 c + 2}$

Step 1.4.3

Factor $2$ out of $2 c + 2 \cdot - 4$ .

$\frac{c - 4}{3 c - 2} + \frac{2 (c - 4)}{- 3 c + 2}$

Step 1.5

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

$\frac{c - 4}{3 c - 2} + \frac{2 (c - 4)}{- (3 c) + 2}$

Step 1.6

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 1.7

Factor $- 1$ out of $- (3 c) - 1 (- 2)$ .

$\frac{c - 4}{3 c - 2} + \frac{2 (c - 4)}{- (3 c - 2)}$

Step 1.8

Move a negative from the denominator of $\frac{2 (c - 4)}{- (3 c - 2)}$ to the numerator.

$\frac{c - 4}{3 c - 2} + \frac{- (2 (c - 4))}{3 c - 2}$

Step 1.9

Combine the numerators over the common denominator.

$\frac{c - 4 - (2 (c - 4))}{3 c - 2}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1$ by $2$ .

$\frac{c - 4 - 2 (c - 4)}{3 c - 2}$

Step 2.2

Apply the distributive property.

$\frac{c - 4 - 2 c - 2 \cdot - 4}{3 c - 2}$

Step 2.3

Multiply $- 2$ by $- 4$ .

$\frac{c - 4 - 2 c + 8}{3 c - 2}$

Step 2.4

Subtract $2 c$ from $c$ .

$\frac{- c - 4 + 8}{3 c - 2}$

Step 2.5

Add $- 4$ and $8$ .

$\frac{- c + 4}{3 c - 2}$

Step 3

Simplify with factoring out.

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Step 3.1

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

$\frac{- (c) + 4}{3 c - 2}$

Step 3.2

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

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

Step 3.3

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

$\frac{- (c - 4)}{3 c - 2}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Rewrite $- (c - 4)$ as $- 1 (c - 4)$ .

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

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{c - 4}{3 c - 2}$