Pre-Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$\frac{5 a - (3 a) - 1 \cdot 2 + 4}{a + 7}$

Step 2.2

Multiply $3$ by $- 1$ .

$\frac{5 a - 3 a - 1 \cdot 2 + 4}{a + 7}$

Step 2.3

Multiply $- 1$ by $2$ .

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

Step 3

Simplify terms.

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Step 3.1

Subtract $3 a$ from $5 a$ .

$\frac{2 a - 2 + 4}{a + 7}$

Step 3.2

Add $- 2$ and $4$ .

$\frac{2 a + 2}{a + 7}$

Step 3.3

Factor $2$ out of $2 a + 2$ .

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Step 3.3.1

Factor $2$ out of $2 a$ .

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

Step 3.3.2

Factor $2$ out of $2$ .

$\frac{2 (a) + 2 (1)}{a + 7}$

Step 3.3.3

Factor $2$ out of $2 (a) + 2 (1)$ .

$\frac{2 (a + 1)}{a + 7}$