Algebra Examples

$\frac{4}{x + 6} + \frac{3}{x + 1}$

Step 1

To write $\frac{4}{x + 6}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{4}{x + 6} \cdot \frac{x + 1}{x + 1} + \frac{3}{x + 1}$

Step 2

To write $\frac{3}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x + 6}{x + 6}$ .

$\frac{4}{x + 6} \cdot \frac{x + 1}{x + 1} + \frac{3}{x + 1} \cdot \frac{x + 6}{x + 6}$

Step 3

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

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Multiply $\frac{4}{x + 6}$ by $\frac{x + 1}{x + 1}$ .

$\frac{4 (x + 1)}{(x + 6) (x + 1)} + \frac{3}{x + 1} \cdot \frac{x + 6}{x + 6}$

Multiply $\frac{3}{x + 1}$ by $\frac{x + 6}{x + 6}$ .

$\frac{4 (x + 1)}{(x + 6) (x + 1)} + \frac{3 (x + 6)}{(x + 1) (x + 6)}$

Reorder the factors of $(x + 6) (x + 1)$ .

$\frac{4 (x + 1)}{(x + 1) (x + 6)} + \frac{3 (x + 6)}{(x + 1) (x + 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 (x + 1) + 3 (x + 6)}{(x + 1) (x + 6)}$

Step 5

Simplify the numerator.

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Apply the distributive property.

$\frac{4 x + 4 \cdot 1 + 3 (x + 6)}{(x + 1) (x + 6)}$

Multiply $4$ by $1$ .

$\frac{4 x + 4 + 3 (x + 6)}{(x + 1) (x + 6)}$

Apply the distributive property.

$\frac{4 x + 4 + 3 x + 3 \cdot 6}{(x + 1) (x + 6)}$

Multiply $3$ by $6$ .

$\frac{4 x + 4 + 3 x + 18}{(x + 1) (x + 6)}$

Add $4 x$ and $3 x$ .

$\frac{7 x + 4 + 18}{(x + 1) (x + 6)}$

Add $4$ and $18$ .

$\frac{7 x + 22}{(x + 1) (x + 6)}$

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