Finite Math Examples

$- 2 + \frac{8 a + 7 x}{6 a} - \frac{6 a - 4 x}{9 a}$

Step 1

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

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Step 1.1

Factor $2$ out of $6 a$ .

$- 2 + \frac{8 a + 7 x}{6 a} - \frac{2 (3 a) - 4 x}{9 a}$

Step 1.2

Factor $2$ out of $- 4 x$ .

$- 2 + \frac{8 a + 7 x}{6 a} - \frac{2 (3 a) + 2 (- 2 x)}{9 a}$

Step 1.3

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

$- 2 + \frac{8 a + 7 x}{6 a} - \frac{2 (3 a - 2 x)}{9 a}$

Step 2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{6 a}{6 a}$ .

$- 2 \cdot \frac{6 a}{6 a} + \frac{8 a + 7 x}{6 a} - \frac{2 (3 a - 2 x)}{9 a}$

Step 3

Simplify terms.

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Step 3.1

Combine $- 2$ and $\frac{6 a}{6 a}$ .

$\frac{- 2 (6 a)}{6 a} + \frac{8 a + 7 x}{6 a} - \frac{2 (3 a - 2 x)}{9 a}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 2 (6 a) + 8 a + 7 x}{6 a} - \frac{2 (3 a - 2 x)}{9 a}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $- 2$ by $6$ .

$\frac{- 12 a + 8 a + 7 x}{6 a} - \frac{2 (3 a - 2 x)}{9 a}$

Step 4.2

Add $- 12 a$ and $8 a$ .

$\frac{- 4 a + 7 x}{6 a} - \frac{2 (3 a - 2 x)}{9 a}$

Step 5

To write $\frac{- 4 a + 7 x}{6 a}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- 4 a + 7 x}{6 a} \cdot \frac{3}{3} - \frac{2 (3 a - 2 x)}{9 a}$

Step 6

To write $- \frac{2 (3 a - 2 x)}{9 a}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{- 4 a + 7 x}{6 a} \cdot \frac{3}{3} - \frac{2 (3 a - 2 x)}{9 a} \cdot \frac{2}{2}$

Step 7

Write each expression with a common denominator of $18 a$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{- 4 a + 7 x}{6 a}$ by $\frac{3}{3}$ .

$\frac{(- 4 a + 7 x) \cdot 3}{6 a \cdot 3} - \frac{2 (3 a - 2 x)}{9 a} \cdot \frac{2}{2}$

Step 7.2

Multiply $3$ by $6$ .

$\frac{(- 4 a + 7 x) \cdot 3}{18 a} - \frac{2 (3 a - 2 x)}{9 a} \cdot \frac{2}{2}$

Step 7.3

Multiply $\frac{2 (3 a - 2 x)}{9 a}$ by $\frac{2}{2}$ .

$\frac{(- 4 a + 7 x) \cdot 3}{18 a} - \frac{2 (3 a - 2 x) \cdot 2}{9 a \cdot 2}$

Step 7.4

Multiply $2$ by $9$ .

$\frac{(- 4 a + 7 x) \cdot 3}{18 a} - \frac{2 (3 a - 2 x) \cdot 2}{18 a}$

Step 8

Combine the numerators over the common denominator.

$\frac{(- 4 a + 7 x) \cdot 3 - 2 (3 a - 2 x) \cdot 2}{18 a}$

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

$\frac{- 4 a \cdot 3 + 7 x \cdot 3 - 2 (3 a - 2 x) \cdot 2}{18 a}$

Step 9.2

Multiply $3$ by $- 4$ .

$\frac{- 12 a + 7 x \cdot 3 - 2 (3 a - 2 x) \cdot 2}{18 a}$

Step 9.3

Multiply $3$ by $7$ .

$\frac{- 12 a + 21 x - 2 (3 a - 2 x) \cdot 2}{18 a}$

Step 9.4

Apply the distributive property.

$\frac{- 12 a + 21 x + (- 2 (3 a) - 2 (- 2 x)) \cdot 2}{18 a}$

Step 9.5

Multiply $3$ by $- 2$ .

$\frac{- 12 a + 21 x + (- 6 a - 2 (- 2 x)) \cdot 2}{18 a}$

Step 9.6

Multiply $- 2$ by $- 2$ .

$\frac{- 12 a + 21 x + (- 6 a + 4 x) \cdot 2}{18 a}$

Step 9.7

Apply the distributive property.

$\frac{- 12 a + 21 x - 6 a \cdot 2 + 4 x \cdot 2}{18 a}$

Step 9.8

Multiply $2$ by $- 6$ .

$\frac{- 12 a + 21 x - 12 a + 4 x \cdot 2}{18 a}$

Step 9.9

Multiply $2$ by $4$ .

$\frac{- 12 a + 21 x - 12 a + 8 x}{18 a}$

Step 9.10

Subtract $12 a$ from $- 12 a$ .

$\frac{- 24 a + 21 x + 8 x}{18 a}$

Step 9.11

Add $21 x$ and $8 x$ .

$\frac{- 24 a + 29 x}{18 a}$

Step 10

Simplify with factoring out.

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Step 10.1

Factor $- 1$ out of $- 24 a$ .

$\frac{- (24 a) + 29 x}{18 a}$

Step 10.2

Factor $- 1$ out of $29 x$ .

$\frac{- (24 a) - (- 29 x)}{18 a}$

Step 10.3

Factor $- 1$ out of $- (24 a) - (- 29 x)$ .

$\frac{- (24 a - 29 x)}{18 a}$

Step 10.4

Simplify the expression.

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Step 10.4.1

Rewrite $- (24 a - 29 x)$ as $- 1 (24 a - 29 x)$ .

$\frac{- 1 (24 a - 29 x)}{18 a}$

Step 10.4.2

Move the negative in front of the fraction.

$- \frac{24 a - 29 x}{18 a}$