Basic Math Examples

$\frac{6}{5 a + 10} + \frac{7}{6 a + 12}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $5$ out of $5 a$ .

$\frac{6}{5 (a) + 10} + \frac{7}{6 a + 12}$

Step 1.1.2

Factor $5$ out of $10$ .

$\frac{6}{5 a + 5 \cdot 2} + \frac{7}{6 a + 12}$

Step 1.1.3

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

$\frac{6}{5 (a + 2)} + \frac{7}{6 a + 12}$

Step 1.2

Factor $6$ out of $6 a + 12$ .

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Step 1.2.1

Factor $6$ out of $6 a$ .

$\frac{6}{5 (a + 2)} + \frac{7}{6 (a) + 12}$

Step 1.2.2

Factor $6$ out of $12$ .

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

Step 1.2.3

Factor $6$ out of $6 a + 6 \cdot 2$ .

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

Step 2

To write $\frac{6}{5 (a + 2)}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Step 3

To write $\frac{7}{6 (a + 2)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 4

Write each expression with a common denominator of $30 (a + 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{6}{5 (a + 2)}$ by $\frac{6}{6}$ .

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

Step 4.2

Multiply $6$ by $5$ .

$\frac{6 \cdot 6}{30 (a + 2)} + \frac{7}{6 (a + 2)} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{7}{6 (a + 2)}$ by $\frac{5}{5}$ .

$\frac{6 \cdot 6}{30 (a + 2)} + \frac{7 \cdot 5}{6 (a + 2) \cdot 5}$

Step 4.4

Multiply $5$ by $6$ .

$\frac{6 \cdot 6}{30 (a + 2)} + \frac{7 \cdot 5}{30 (a + 2)}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 \cdot 6 + 7 \cdot 5}{30 (a + 2)}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $6$ by $6$ .

$\frac{36 + 7 \cdot 5}{30 (a + 2)}$

Step 6.2

Multiply $7$ by $5$ .

$\frac{36 + 35}{30 (a + 2)}$

Step 6.3

Add $36$ and $35$ .

$\frac{71}{30 (a + 2)}$