Basic Math Examples

$\frac{\frac{6 w^{4}}{w^{2} + 2 w - 24}}{\frac{3 w^{2}}{w - 4}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 w^{4}}{w^{2} + 2 w - 24} \cdot \frac{w - 4}{3 w^{2}}$

Step 2

Cancel the common factor of $3 w^{2}$ .

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Step 2.1

Factor $3 w^{2}$ out of $6 w^{4}$ .

$\frac{3 w^{2} (2 w^{2})}{w^{2} + 2 w - 24} \cdot \frac{w - 4}{3 w^{2}}$

Step 2.2

Cancel the common factor.

$\frac{3 w^{2} (2 w^{2})}{w^{2} + 2 w - 24} \cdot \frac{w - 4}{3 w^{2}}$

Step 2.3

Rewrite the expression.

$\frac{2 w^{2}}{w^{2} + 2 w - 24} (w - 4)$

Step 3

Factor $w^{2} + 2 w - 24$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 24$ and whose sum is $2$ .

$- 4, 6$

Step 3.2

Write the factored form using these integers.

$\frac{2 w^{2}}{(w - 4) (w + 6)} (w - 4)$

Step 4

Cancel the common factor of $w - 4$ .

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Step 4.1

Cancel the common factor.

$\frac{2 w^{2}}{(w - 4) (w + 6)} (w - 4)$

Step 4.2

Rewrite the expression.

$\frac{2 w^{2}}{w + 6}$