Algebra Examples

$\frac{7}{x + 1} + \frac{2}{x + 6}$

To write $\frac{7}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x + 6}{x + 6}$ .

$\frac{7}{x + 1} \cdot \frac{x + 6}{x + 6} + \frac{2}{x + 6}$

To write $\frac{2}{x + 6}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{7}{x + 1} \cdot \frac{x + 6}{x + 6} + \frac{2}{x + 6} \cdot \frac{x + 1}{x + 1}$

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

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Multiply $\frac{7}{x + 1}$ and $\frac{x + 6}{x + 6}$ .

$\frac{7 (x + 6)}{(x + 1) (x + 6)} + \frac{2}{x + 6} \cdot \frac{x + 1}{x + 1}$

Multiply $\frac{2}{x + 6}$ and $\frac{x + 1}{x + 1}$ .

$\frac{7 (x + 6)}{(x + 1) (x + 6)} + \frac{2 (x + 1)}{(x + 6) (x + 1)}$

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

$\frac{7 (x + 6)}{(x + 1) (x + 6)} + \frac{2 (x + 1)}{(x + 1) (x + 6)}$

Combine the numerators over the common denominator.

$\frac{7 (x + 6) + 2 (x + 1)}{(x + 1) (x + 6)}$

Simplify the numerator.

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Apply the distributive property.

$\frac{7 x + 7 \cdot 6 + 2 (x + 1)}{(x + 1) (x + 6)}$

Multiply $7$ by $6$ .

$\frac{7 x + 42 + 2 (x + 1)}{(x + 1) (x + 6)}$

Apply the distributive property.

$\frac{7 x + 42 + 2 x + 2 \cdot 1}{(x + 1) (x + 6)}$

Multiply $2$ by $1$ .

$\frac{7 x + 42 + 2 x + 2}{(x + 1) (x + 6)}$

Add $7 x$ and $2 x$ .

$\frac{9 x + 42 + 2}{(x + 1) (x + 6)}$

Add $42$ and $2$ .

$\frac{9 x + 44}{(x + 1) (x + 6)}$

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