Basic Math Examples

$\frac{\frac{11 - w}{30 w^{2}}}{\frac{w - 11}{5 w^{6}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{11 - w}{30 w^{2}} \cdot \frac{5 w^{6}}{w - 11}$

Step 2

Cancel the common factor of $5 w^{2}$ .

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Step 2.1

Factor $5 w^{2}$ out of $30 w^{2}$ .

$\frac{11 - w}{5 w^{2} (6)} \cdot \frac{5 w^{6}}{w - 11}$

Step 2.2

Factor $5 w^{2}$ out of $5 w^{6}$ .

$\frac{11 - w}{5 w^{2} (6)} \cdot \frac{5 w^{2} (w^{4})}{w - 11}$

Step 2.3

Cancel the common factor.

$\frac{11 - w}{5 w^{2} \cdot 6} \cdot \frac{5 w^{2} w^{4}}{w - 11}$

Step 2.4

Rewrite the expression.

$\frac{11 - w}{6} \cdot \frac{w^{4}}{w - 11}$

Step 3

Multiply $\frac{11 - w}{6}$ by $\frac{w^{4}}{w - 11}$ .

$\frac{(11 - w) w^{4}}{6 (w - 11)}$

Step 4

Cancel the common factor of $11 - w$ and $w - 11$ .

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Step 4.1

Rewrite $11$ as $- 1 (- 11)$ .

$\frac{(- 1 (- 11) - w) w^{4}}{6 (w - 11)}$

Step 4.2

Factor $- 1$ out of $- w$ .

$\frac{(- 1 (- 11) - (w)) w^{4}}{6 (w - 11)}$

Step 4.3

Factor $- 1$ out of $- 1 (- 11) - (w)$ .

$\frac{- 1 (- 11 + w) w^{4}}{6 (w - 11)}$

Step 4.4

Reorder terms.

$\frac{- 1 (w - 11) w^{4}}{6 (w - 11)}$

Step 4.5

Cancel the common factor.

$\frac{- 1 (w - 11) w^{4}}{6 (w - 11)}$

Step 4.6

Rewrite the expression.

$\frac{- 1 w^{4}}{6}$

Step 5

Move the negative in front of the fraction.

$- \frac{w^{4}}{6}$