Basic Math Examples

$\frac{(- r - 6) + 8}{r^{2} - 36}$

Step 1

Add $- 6$ and $8$ .

$\frac{- r + 2}{r^{2} - 36}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $36$ as $6^{2}$ .

$\frac{- r + 2}{r^{2} - 6^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = r$ and $b = 6$ .

$\frac{- r + 2}{(r + 6) (r - 6)}$

Step 3

Simplify with factoring out.

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Step 3.1

Factor $- 1$ out of $- r$ .

$\frac{- (r) + 2}{(r + 6) (r - 6)}$

Step 3.2

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{- (r) - 1 (- 2)}{(r + 6) (r - 6)}$

Step 3.3

Factor $- 1$ out of $- (r) - 1 (- 2)$ .

$\frac{- (r - 2)}{(r + 6) (r - 6)}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Rewrite $- (r - 2)$ as $- 1 (r - 2)$ .

$\frac{- 1 (r - 2)}{(r + 6) (r - 6)}$

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{r - 2}{(r + 6) (r - 6)}$