Precalculus Examples

$\frac{4}{3 a - 6} + \frac{7}{5 a - 10}$

Step 1

Simplify each term.

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Step 1.1

Factor $3$ out of $3 a - 6$ .

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Step 1.1.1

Factor $3$ out of $3 a$ .

$\frac{4}{3 (a) - 6} + \frac{7}{5 a - 10}$

Step 1.1.2

Factor $3$ out of $- 6$ .

$\frac{4}{3 a + 3 \cdot - 2} + \frac{7}{5 a - 10}$

Step 1.1.3

Factor $3$ out of $3 a + 3 \cdot - 2$ .

$\frac{4}{3 (a - 2)} + \frac{7}{5 a - 10}$

Step 1.2

Factor $5$ out of $5 a - 10$ .

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Step 1.2.1

Factor $5$ out of $5 a$ .

$\frac{4}{3 (a - 2)} + \frac{7}{5 (a) - 10}$

Step 1.2.2

Factor $5$ out of $- 10$ .

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

Step 1.2.3

Factor $5$ out of $5 a + 5 \cdot - 2$ .

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

Step 2

To write $\frac{4}{3 (a - 2)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 3

To write $\frac{7}{5 (a - 2)}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4

Write each expression with a common denominator of $15 (a - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{4}{3 (a - 2)}$ by $\frac{5}{5}$ .

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

Step 4.2

Multiply $5$ by $3$ .

$\frac{4 \cdot 5}{15 (a - 2)} + \frac{7}{5 (a - 2)} \cdot \frac{3}{3}$

Step 4.3

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

$\frac{4 \cdot 5}{15 (a - 2)} + \frac{7 \cdot 3}{5 (a - 2) \cdot 3}$

Step 4.4

Multiply $3$ by $5$ .

$\frac{4 \cdot 5}{15 (a - 2)} + \frac{7 \cdot 3}{15 (a - 2)}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 + 7 \cdot 3}{15 (a - 2)}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $5$ .

$\frac{20 + 7 \cdot 3}{15 (a - 2)}$

Step 6.2

Multiply $7$ by $3$ .

$\frac{20 + 21}{15 (a - 2)}$

Step 6.3

Add $20$ and $21$ .

$\frac{41}{15 (a - 2)}$