Pre-Algebra Examples

$\frac{6 - m}{m^{3} - 216}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $216$ as $6^{3}$ .

$\frac{6 - m}{m^{3} - 6^{3}}$

Step 1.2

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = m$ and $b = 6$ .

$\frac{6 - m}{(m - 6) (m^{2} + m \cdot 6 + 6^{2})}$

Step 1.3

Simplify.

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Step 1.3.1

Move $6$ to the left of $m$ .

$\frac{6 - m}{(m - 6) (m^{2} + 6 \cdot m + 6^{2})}$

Step 1.3.2

Raise $6$ to the power of $2$ .

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $6 - m$ and $m - 6$ .

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Step 2.1.1

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{- 1 (- 6) - m}{(m - 6) (m^{2} + 6 m + 36)}$

Step 2.1.2

Factor $- 1$ out of $- m$ .

$\frac{- 1 (- 6) - (m)}{(m - 6) (m^{2} + 6 m + 36)}$

Step 2.1.3

Factor $- 1$ out of $- 1 (- 6) - (m)$ .

$\frac{- 1 (- 6 + m)}{(m - 6) (m^{2} + 6 m + 36)}$

Step 2.1.4

Reorder terms.

$\frac{- 1 (m - 6)}{(m - 6) (m^{2} + 6 m + 36)}$

Step 2.1.5

Cancel the common factor.

$\frac{- 1 (m - 6)}{(m - 6) (m^{2} + 6 m + 36)}$

Step 2.1.6

Rewrite the expression.

$\frac{- 1}{m^{2} + 6 m + 36}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{m^{2} + 6 m + 36}$