Precalculus Examples

$\frac{9}{x + 8} - \frac{2}{x + 7}$

Step 1

To write

$\frac{9}{x + 8}$ as a fraction with a common denominator, multiply by

$\frac{x + 7}{x + 7}$ .

$\frac{9}{x + 8} \cdot \frac{x + 7}{x + 7} - \frac{2}{x + 7}$

Step 2

To write

$- \frac{2}{x + 7}$ as a fraction with a common denominator, multiply by

$\frac{x + 8}{x + 8}$ .

$\frac{9}{x + 8} \cdot \frac{x + 7}{x + 7} - \frac{2}{x + 7} \cdot \frac{x + 8}{x + 8}$

Step 3

Write each expression with a common denominator of

$(x + 8) (x + 7)$ , by multiplying each by an appropriate factor of

$1$ .

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Step 3.1

Multiply

$\frac{9}{x + 8}$ by

$\frac{x + 7}{x + 7}$ .

$\frac{9 (x + 7)}{(x + 8) (x + 7)} - \frac{2}{x + 7} \cdot \frac{x + 8}{x + 8}$

Step 3.2

Multiply

$\frac{2}{x + 7}$ by

$\frac{x + 8}{x + 8}$ .

$\frac{9 (x + 7)}{(x + 8) (x + 7)} - \frac{2 (x + 8)}{(x + 7) (x + 8)}$

Step 3.3

Reorder the factors of

$(x + 8) (x + 7)$ .

$\frac{9 (x + 7)}{(x + 7) (x + 8)} - \frac{2 (x + 8)}{(x + 7) (x + 8)}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 (x + 7) - 2 (x + 8)}{(x + 7) (x + 8)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{9 x + 9 \cdot 7 - 2 (x + 8)}{(x + 7) (x + 8)}$

Step 5.2

Multiply

$9$ by

$7$ .

$\frac{9 x + 63 - 2 (x + 8)}{(x + 7) (x + 8)}$

Step 5.3

Apply the distributive property.

$\frac{9 x + 63 - 2 x - 2 \cdot 8}{(x + 7) (x + 8)}$

Step 5.4

Multiply

$- 2$ by

$8$ .

$\frac{9 x + 63 - 2 x - 16}{(x + 7) (x + 8)}$

Step 5.5

Subtract

$2 x$ from

$9 x$ .

$\frac{7 x + 63 - 16}{(x + 7) (x + 8)}$

Step 5.6

Subtract

$16$ from

$63$ .

$\frac{7 x + 47}{(x + 7) (x + 8)}$

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