Algebra Examples

$\frac{6 a - 4}{7 a - 5} - 3$

Step 1

Factor $2$ out of $6 a - 4$ .

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Step 1.1

Factor $2$ out of $6 a$ .

$\frac{2 (3 a) - 4}{7 a - 5} - 3$

Step 1.2

Factor $2$ out of $- 4$ .

$\frac{2 (3 a) + 2 (- 2)}{7 a - 5} - 3$

Step 1.3

Factor $2$ out of $2 (3 a) + 2 (- 2)$ .

$\frac{2 (3 a - 2)}{7 a - 5} - 3$

Step 2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{7 a - 5}{7 a - 5}$ .

$\frac{2 (3 a - 2)}{7 a - 5} - 3 \cdot \frac{7 a - 5}{7 a - 5}$

Step 3

Simplify terms.

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Step 3.1

Combine $- 3$ and $\frac{7 a - 5}{7 a - 5}$ .

$\frac{2 (3 a - 2)}{7 a - 5} + \frac{- 3 (7 a - 5)}{7 a - 5}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 (3 a - 2) - 3 (7 a - 5)}{7 a - 5}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{2 (3 a) + 2 \cdot - 2 - 3 (7 a - 5)}{7 a - 5}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{6 a + 2 \cdot - 2 - 3 (7 a - 5)}{7 a - 5}$

Step 4.3

Multiply $2$ by $- 2$ .

$\frac{6 a - 4 - 3 (7 a - 5)}{7 a - 5}$

Step 4.4

Apply the distributive property.

$\frac{6 a - 4 - 3 (7 a) - 3 \cdot - 5}{7 a - 5}$

Step 4.5

Multiply $7$ by $- 3$ .

$\frac{6 a - 4 - 21 a - 3 \cdot - 5}{7 a - 5}$

Step 4.6

Multiply $- 3$ by $- 5$ .

$\frac{6 a - 4 - 21 a + 15}{7 a - 5}$

Step 4.7

Subtract $21 a$ from $6 a$ .

$\frac{- 15 a - 4 + 15}{7 a - 5}$

Step 4.8

Add $- 4$ and $15$ .

$\frac{- 15 a + 11}{7 a - 5}$

Step 5

Simplify with factoring out.

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Step 5.1

Factor $- 1$ out of $- 15 a$ .

$\frac{- (15 a) + 11}{7 a - 5}$

Step 5.2

Rewrite $11$ as $- 1 (- 11)$ .

$\frac{- (15 a) - 1 (- 11)}{7 a - 5}$

Step 5.3

Factor $- 1$ out of $- (15 a) - 1 (- 11)$ .

$\frac{- (15 a - 11)}{7 a - 5}$

Step 5.4

Simplify the expression.

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Step 5.4.1

Rewrite $- (15 a - 11)$ as $- 1 (15 a - 11)$ .

$\frac{- 1 (15 a - 11)}{7 a - 5}$

Step 5.4.2

Move the negative in front of the fraction.

$- \frac{15 a - 11}{7 a - 5}$