Algebra Examples

$\frac{2 m + 4}{8} + \frac{m + 2}{6}$

Step 1

Cancel the common factor of $2 m + 4$ and $8$ .

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Step 1.1

Factor $2$ out of $2 m$ .

$\frac{2 (m) + 4}{8} + \frac{m + 2}{6}$

Step 1.2

Factor $2$ out of $4$ .

$\frac{2 m + 2 \cdot 2}{8} + \frac{m + 2}{6}$

Step 1.3

Factor $2$ out of $2 m + 2 \cdot 2$ .

$\frac{2 (m + 2)}{8} + \frac{m + 2}{6}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $8$ .

$\frac{2 (m + 2)}{2 (4)} + \frac{m + 2}{6}$

Step 1.4.2

Cancel the common factor.

$\frac{2 (m + 2)}{2 \cdot 4} + \frac{m + 2}{6}$

Step 1.4.3

Rewrite the expression.

$\frac{m + 2}{4} + \frac{m + 2}{6}$

Step 2

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

$\frac{m + 2}{4} \cdot \frac{3}{3} + \frac{m + 2}{6}$

Step 3

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

$\frac{m + 2}{4} \cdot \frac{3}{3} + \frac{m + 2}{6} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{m + 2}{4}$ by $\frac{3}{3}$ .

$\frac{(m + 2) \cdot 3}{4 \cdot 3} + \frac{m + 2}{6} \cdot \frac{2}{2}$

Step 4.2

Multiply $4$ by $3$ .

$\frac{(m + 2) \cdot 3}{12} + \frac{m + 2}{6} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{m + 2}{6}$ by $\frac{2}{2}$ .

$\frac{(m + 2) \cdot 3}{12} + \frac{(m + 2) \cdot 2}{6 \cdot 2}$

Step 4.4

Multiply $6$ by $2$ .

$\frac{(m + 2) \cdot 3}{12} + \frac{(m + 2) \cdot 2}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{(m + 2) \cdot 3 + (m + 2) \cdot 2}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{m \cdot 3 + 2 \cdot 3 + (m + 2) \cdot 2}{12}$

Step 6.2

Move $3$ to the left of $m$ .

$\frac{3 \cdot m + 2 \cdot 3 + (m + 2) \cdot 2}{12}$

Step 6.3

Multiply $2$ by $3$ .

$\frac{3 \cdot m + 6 + (m + 2) \cdot 2}{12}$

Step 6.4

Apply the distributive property.

$\frac{3 m + 6 + m \cdot 2 + 2 \cdot 2}{12}$

Step 6.5

Move $2$ to the left of $m$ .

$\frac{3 m + 6 + 2 \cdot m + 2 \cdot 2}{12}$

Step 6.6

Multiply $2$ by $2$ .

$\frac{3 m + 6 + 2 \cdot m + 4}{12}$

Step 6.7

Add $3 m$ and $2 m$ .

$\frac{5 m + 6 + 4}{12}$

Step 6.8

Add $6$ and $4$ .

$\frac{5 m + 10}{12}$

Step 6.9

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

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Step 6.9.1

Factor $5$ out of $5 m$ .

$\frac{5 (m) + 10}{12}$

Step 6.9.2

Factor $5$ out of $10$ .

$\frac{5 m + 5 \cdot 2}{12}$

Step 6.9.3

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

$\frac{5 (m + 2)}{12}$