Simplify (m/4-1/m)/(1/(3m)+1/6)

$\frac{\frac{m}{4} - \frac{1}{m}}{\frac{1}{3 m} + \frac{1}{6}}$

Multiply the numerator and denominator of the complex fraction by $12 m$ .

Multiply $\frac{\frac{m}{4} - \frac{1}{m}}{\frac{1}{3 m} + \frac{1}{6}}$ by $\frac{12 m}{12 m}$ .

$\frac{12 m}{12 m} \cdot \frac{\frac{m}{4} - \frac{1}{m}}{\frac{1}{3 m} + \frac{1}{6}}$

Combine.

$\frac{12 m (\frac{m}{4} - \frac{1}{m})}{12 m (\frac{1}{3 m} + \frac{1}{6})}$

Apply the distributive property.

$\frac{12 m \frac{m}{4} + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Simplify by cancelling.

Cancel the common factor of $4$ .

Factor $4$ out of $12 m$ .

$\frac{4 (3 m) \frac{m}{4} + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Cancel the common factor.

$\frac{4 (3 m) \frac{m}{4} + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Rewrite the expression.

$\frac{3 m \cdot m + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Raise $m$ to the power of $1$ .

$\frac{3 (m^{1} m) + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Raise $m$ to the power of $1$ .

$\frac{3 (m^{1} m^{1}) + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 m^{1 + 1} + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Add $1$ and $1$ .

$\frac{3 m^{2} + 12 m (- \frac{1}{m})}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Cancel the common factor of $m$ .

Move the leading negative in $- \frac{1}{m}$ into the numerator.

$\frac{3 m^{2} + 12 m \frac{- 1}{m}}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Factor $m$ out of $12 m$ .

$\frac{3 m^{2} + m \cdot 12 \frac{- 1}{m}}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Cancel the common factor.

$\frac{3 m^{2} + m \cdot 12 \frac{- 1}{m}}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Rewrite the expression.

$\frac{3 m^{2} + 12 \cdot - 1}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Multiply $12$ by $- 1$ .

$\frac{3 m^{2} - 12}{12 m \frac{1}{3 m} + 12 m \frac{1}{6}}$

Cancel the common factor of $3 m$ .

Factor $3 m$ out of $12 m$ .

$\frac{3 m^{2} - 12}{3 m (4) \frac{1}{3 m} + 12 m \frac{1}{6}}$

Cancel the common factor.

$\frac{3 m^{2} - 12}{3 m \cdot 4 \frac{1}{3 m} + 12 m \frac{1}{6}}$

Rewrite the expression.

$\frac{3 m^{2} - 12}{4 + 12 m \frac{1}{6}}$

Cancel the common factor of $6$ .

Factor $6$ out of $12 m$ .

$\frac{3 m^{2} - 12}{4 + 6 (2 m) \frac{1}{6}}$

Cancel the common factor.

$\frac{3 m^{2} - 12}{4 + 6 (2 m) \frac{1}{6}}$

Rewrite the expression.

$\frac{3 m^{2} - 12}{4 + 2 m}$

Simplify the numerator.

Factor $3$ out of $3 m^{2} - 12$ .

Factor $3$ out of $3 m^{2}$ .

$\frac{3 (m^{2}) - 12}{4 + 2 m}$

Factor $3$ out of $- 12$ .

$\frac{3 m^{2} + 3 \cdot - 4}{4 + 2 m}$

Factor $3$ out of $3 m^{2} + 3 \cdot - 4$ .

$\frac{3 (m^{2} - 4)}{4 + 2 m}$

Rewrite $4$ as $2^{2}$ .

$\frac{3 (m^{2} - 2^{2})}{4 + 2 m}$

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

$\frac{3 (m + 2) (m - 2)}{4 + 2 m}$

Simplify terms.

Factor $2$ out of $4 + 2 m$ .

Factor $2$ out of $4$ .

$\frac{3 (m + 2) (m - 2)}{2 \cdot 2 + 2 m}$

Factor $2$ out of $2 \cdot 2 + 2 m$ .

$\frac{3 (m + 2) (m - 2)}{2 (2 + m)}$

Cancel the common factor of $m + 2$ and $2 + m$ .

Reorder terms.

$\frac{3 (m + 2) (m - 2)}{2 (m + 2)}$

Cancel the common factor.

$\frac{3 (m + 2) (m - 2)}{2 (m + 2)}$

Rewrite the expression.

$\frac{3 (m - 2)}{2}$

Simplify (m/4-1/m)/(1/(3m)+1/6)

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