Basic Math Examples

$\frac{1}{1 - \frac{a - 8}{5}}$

Step 1

Simplify the denominator.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{1}{\frac{5}{5} - \frac{a - 8}{5}}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{\frac{5 - (a - 8)}{5}}$

Step 1.3

Rewrite $\frac{5 - (a - 8)}{5}$ in a factored form.

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Step 1.3.1

Apply the distributive property.

$\frac{1}{\frac{5 - a - - 8}{5}}$

Step 1.3.2

Multiply $- 1$ by $- 8$ .

$\frac{1}{\frac{5 - a + 8}{5}}$

Step 1.3.3

Add $5$ and $8$ .

$\frac{1}{\frac{- a + 13}{5}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{5}{- a + 13}$

Step 3

Multiply $\frac{5}{- a + 13}$ by $1$ .

$\frac{5}{- a + 13}$

Step 4

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

$\frac{5}{- (a) + 13}$

Step 5

Rewrite $13$ as $- 1 (- 13)$ .

$\frac{5}{- (a) - 1 (- 13)}$

Step 6

Factor $- 1$ out of $- (a) - 1 (- 13)$ .

$\frac{5}{- (a - 13)}$

Step 7

Rewrite negatives.

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Step 7.1

Rewrite $- (a - 13)$ as $- 1 (a - 13)$ .

$\frac{5}{- 1 (a - 13)}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{5}{a - 13}$