Basic Math Examples

$\frac{15 u^{5} w^{4}}{10 u^{3} - 25 u^{2} v^{2}}$

Step 1

Factor $5 u^{2}$ out of $10 u^{3} - 25 u^{2} v^{2}$ .

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Step 1.1

Factor $5 u^{2}$ out of $10 u^{3}$ .

$\frac{15 u^{5} w^{4}}{5 u^{2} (2 u) - 25 u^{2} v^{2}}$

Step 1.2

Factor $5 u^{2}$ out of $- 25 u^{2} v^{2}$ .

$\frac{15 u^{5} w^{4}}{5 u^{2} (2 u) + 5 u^{2} (- 5 v^{2})}$

Step 1.3

Factor $5 u^{2}$ out of $5 u^{2} (2 u) + 5 u^{2} (- 5 v^{2})$ .

$\frac{15 u^{5} w^{4}}{5 u^{2} (2 u - 5 v^{2})}$

Step 2

Cancel the common factor of $15$ and $5$ .

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Step 2.1

Factor $5$ out of $15 u^{5} w^{4}$ .

$\frac{5 (3 u^{5} w^{4})}{5 u^{2} (2 u - 5 v^{2})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $5 u^{2} (2 u - 5 v^{2})$ .

$\frac{5 (3 u^{5} w^{4})}{5 (u^{2} (2 u - 5 v^{2}))}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (3 u^{5} w^{4})}{5 (u^{2} (2 u - 5 v^{2}))}$

Step 2.2.3

Rewrite the expression.

$\frac{3 u^{5} w^{4}}{u^{2} (2 u - 5 v^{2})}$

Step 3

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

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Step 3.1

Factor $u^{2}$ out of $3 u^{5} w^{4}$ .

$\frac{u^{2} (3 u^{3} w^{4})}{u^{2} (2 u - 5 v^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Cancel the common factor.

$\frac{u^{2} (3 u^{3} w^{4})}{u^{2} (2 u - 5 v^{2})}$

Step 3.2.2

Rewrite the expression.

$\frac{3 u^{3} w^{4}}{2 u - 5 v^{2}}$