Basic Math Examples

$\frac{5}{2 y + 8} + \frac{7}{3 y + 12}$

Step 1

Simplify each term.

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Step 1.1

Factor $2$ out of $2 y + 8$ .

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Step 1.1.1

Factor $2$ out of $2 y$ .

$\frac{5}{2 (y) + 8} + \frac{7}{3 y + 12}$

Step 1.1.2

Factor $2$ out of $8$ .

$\frac{5}{2 y + 2 \cdot 4} + \frac{7}{3 y + 12}$

Step 1.1.3

Factor $2$ out of $2 y + 2 \cdot 4$ .

$\frac{5}{2 (y + 4)} + \frac{7}{3 y + 12}$

Step 1.2

Factor $3$ out of $3 y + 12$ .

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Step 1.2.1

Factor $3$ out of $3 y$ .

$\frac{5}{2 (y + 4)} + \frac{7}{3 (y) + 12}$

Step 1.2.2

Factor $3$ out of $12$ .

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

Step 1.2.3

Factor $3$ out of $3 y + 3 \cdot 4$ .

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

Step 2

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

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

Step 3

To write $\frac{7}{3 (y + 4)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4

Write each expression with a common denominator of $6 (y + 4)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{2 (y + 4)}$ by $\frac{3}{3}$ .

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

Step 4.2

Multiply $3$ by $2$ .

$\frac{5 \cdot 3}{6 (y + 4)} + \frac{7}{3 (y + 4)} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{7}{3 (y + 4)}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{6 (y + 4)} + \frac{7 \cdot 2}{3 (y + 4) \cdot 2}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6 (y + 4)} + \frac{7 \cdot 2}{6 (y + 4)}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 7 \cdot 2}{6 (y + 4)}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $3$ .

$\frac{15 + 7 \cdot 2}{6 (y + 4)}$

Step 6.2

Multiply $7$ by $2$ .

$\frac{15 + 14}{6 (y + 4)}$

Step 6.3

Add $15$ and $14$ .

$\frac{29}{6 (y + 4)}$