Algebra Examples

$\frac{3}{x + 7} + \frac{4}{x - 8}$

Step 1

To write $\frac{3}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

$\frac{3}{x + 7} \cdot \frac{x - 8}{x - 8} + \frac{4}{x - 8}$

Step 2

To write $\frac{4}{x - 8}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$\frac{3}{x + 7} \cdot \frac{x - 8}{x - 8} + \frac{4}{x - 8} \cdot \frac{x + 7}{x + 7}$

Step 3

Write each expression with a common denominator of $(x + 7) (x - 8)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{x + 7}$ by $\frac{x - 8}{x - 8}$ .

$\frac{3 (x - 8)}{(x + 7) (x - 8)} + \frac{4}{x - 8} \cdot \frac{x + 7}{x + 7}$

Step 3.2

Multiply $\frac{4}{x - 8}$ by $\frac{x + 7}{x + 7}$ .

$\frac{3 (x - 8)}{(x + 7) (x - 8)} + \frac{4 (x + 7)}{(x - 8) (x + 7)}$

Step 3.3

Reorder the factors of $(x - 8) (x + 7)$ .

$\frac{3 (x - 8)}{(x + 7) (x - 8)} + \frac{4 (x + 7)}{(x + 7) (x - 8)}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (x - 8) + 4 (x + 7)}{(x + 7) (x - 8)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{3 x + 3 \cdot - 8 + 4 (x + 7)}{(x + 7) (x - 8)}$

Step 5.2

Multiply $3$ by $- 8$ .

$\frac{3 x - 24 + 4 (x + 7)}{(x + 7) (x - 8)}$

Step 5.3

Apply the distributive property.

$\frac{3 x - 24 + 4 x + 4 \cdot 7}{(x + 7) (x - 8)}$

Step 5.4

Multiply $4$ by $7$ .

$\frac{3 x - 24 + 4 x + 28}{(x + 7) (x - 8)}$

Step 5.5

Add $3 x$ and $4 x$ .

$\frac{7 x - 24 + 28}{(x + 7) (x - 8)}$

Step 5.6

Add $- 24$ and $28$ .

$\frac{7 x + 4}{(x + 7) (x - 8)}$