Basic Math Examples

$\frac{1}{\frac{1}{a - 2} - 4}$

Step 1

Simplify the denominator.

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Step 1.1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{a - 2}{a - 2}$ .

$\frac{1}{\frac{1}{a - 2} - 4 \cdot \frac{a - 2}{a - 2}}$

Step 1.2

Combine $- 4$ and $\frac{a - 2}{a - 2}$ .

$\frac{1}{\frac{1}{a - 2} + \frac{- 4 (a - 2)}{a - 2}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{1}{\frac{1 - 4 (a - 2)}{a - 2}}$

Step 1.4

Rewrite $\frac{1 - 4 (a - 2)}{a - 2}$ in a factored form.

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Step 1.4.1

Apply the distributive property.

$\frac{1}{\frac{1 - 4 a - 4 \cdot - 2}{a - 2}}$

Step 1.4.2

Multiply $- 4$ by $- 2$ .

$\frac{1}{\frac{1 - 4 a + 8}{a - 2}}$

Step 1.4.3

Add $1$ and $8$ .

$\frac{1}{\frac{- 4 a + 9}{a - 2}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{a - 2}{- 4 a + 9}$

Step 3

Multiply $\frac{a - 2}{- 4 a + 9}$ by $1$ .

$\frac{a - 2}{- 4 a + 9}$

Step 4

Factor $- 1$ out of $- 4 a$ .

$\frac{a - 2}{- (4 a) + 9}$

Step 5

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

$\frac{a - 2}{- (4 a) - 1 (- 9)}$

Step 6

Factor $- 1$ out of $- (4 a) - 1 (- 9)$ .

$\frac{a - 2}{- (4 a - 9)}$

Step 7

Rewrite negatives.

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Step 7.1

Rewrite $- (4 a - 9)$ as $- 1 (4 a - 9)$ .

$\frac{a - 2}{- 1 (4 a - 9)}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{a - 2}{4 a - 9}$