Precalculus Examples

$\frac{7}{\frac{7}{x - 9} - 9}$

Step 1

Simplify the denominator.

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Step 1.1

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{x - 9}{x - 9}$ .

$\frac{7}{\frac{7}{x - 9} - 9 \cdot \frac{x - 9}{x - 9}}$

Step 1.2

Combine $- 9$ and $\frac{x - 9}{x - 9}$ .

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

Step 1.3

Combine the numerators over the common denominator.

$\frac{7}{\frac{7 - 9 (x - 9)}{x - 9}}$

Step 1.4

Rewrite $\frac{7 - 9 (x - 9)}{x - 9}$ in a factored form.

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Step 1.4.1

Apply the distributive property.

$\frac{7}{\frac{7 - 9 x - 9 \cdot - 9}{x - 9}}$

Step 1.4.2

Multiply $- 9$ by $- 9$ .

$\frac{7}{\frac{7 - 9 x + 81}{x - 9}}$

Step 1.4.3

Add $7$ and $81$ .

$\frac{7}{\frac{- 9 x + 88}{x - 9}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$7 \frac{x - 9}{- 9 x + 88}$

Step 3

Combine $7$ and $\frac{x - 9}{- 9 x + 88}$ .

$\frac{7 (x - 9)}{- 9 x + 88}$

Step 4

Factor $- 1$ out of $- 9 x$ .

$\frac{7 (x - 9)}{- (9 x) + 88}$

Step 5

Rewrite $88$ as $- 1 (- 88)$ .

$\frac{7 (x - 9)}{- (9 x) - 1 (- 88)}$

Step 6

Factor $- 1$ out of $- (9 x) - 1 (- 88)$ .

$\frac{7 (x - 9)}{- (9 x - 88)}$

Step 7

Rewrite negatives.

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Step 7.1

Rewrite $- (9 x - 88)$ as $- 1 (9 x - 88)$ .

$\frac{7 (x - 9)}{- 1 (9 x - 88)}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{7 (x - 9)}{9 x - 88}$