Basic Math Examples

$\frac{7}{3} - \frac{8}{12 a - 8}$

Step 1

Cancel the common factor of $8$ and $12 a - 8$ .

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Step 1.1

Factor $4$ out of $8$ .

$\frac{7}{3} - \frac{4 (2)}{12 a - 8}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $12 a$ .

$\frac{7}{3} - \frac{4 (2)}{4 (3 a) - 8}$

Step 1.2.2

Factor $4$ out of $- 8$ .

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

Step 1.2.3

Factor $4$ out of $4 (3 a) + 4 (- 2)$ .

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

Step 1.2.4

Cancel the common factor.

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

Step 1.2.5

Rewrite the expression.

$\frac{7}{3} - \frac{2}{3 a - 2}$

Step 2

To write $\frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{3 a - 2}{3 a - 2}$ .

$\frac{7}{3} \cdot \frac{3 a - 2}{3 a - 2} - \frac{2}{3 a - 2}$

Step 3

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

$\frac{7}{3} \cdot \frac{3 a - 2}{3 a - 2} - \frac{2}{3 a - 2} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $3 (3 a - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{3}$ by $\frac{3 a - 2}{3 a - 2}$ .

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

Step 4.2

Multiply $\frac{2}{3 a - 2}$ by $\frac{3}{3}$ .

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

Step 4.3

Reorder the factors of $(3 a - 2) \cdot 3$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

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

Step 6.2

Multiply $3$ by $7$ .

$\frac{21 a + 7 \cdot - 2 - 2 \cdot 3}{3 (3 a - 2)}$

Step 6.3

Multiply $7$ by $- 2$ .

$\frac{21 a - 14 - 2 \cdot 3}{3 (3 a - 2)}$

Step 6.4

Multiply $- 2$ by $3$ .

$\frac{21 a - 14 - 6}{3 (3 a - 2)}$

Step 6.5

Subtract $6$ from $- 14$ .

$\frac{21 a - 20}{3 (3 a - 2)}$