Finite Math Examples

$\frac{5 m^{3} + 5 m^{2}}{15 m^{2} + 10 m}$

Step 1

Factor $5 m^{2}$ out of $5 m^{3} + 5 m^{2}$ .

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Step 1.1

Factor $5 m^{2}$ out of $5 m^{3}$ .

$\frac{5 m^{2} (m) + 5 m^{2}}{15 m^{2} + 10 m}$

Step 1.2

Factor $5 m^{2}$ out of $5 m^{2}$ .

$\frac{5 m^{2} (m) + 5 m^{2} (1)}{15 m^{2} + 10 m}$

Step 1.3

Factor $5 m^{2}$ out of $5 m^{2} (m) + 5 m^{2} (1)$ .

$\frac{5 m^{2} (m + 1)}{15 m^{2} + 10 m}$

$\frac{5 m^{2} (m + 1)}{15 m^{2} + 10 m}$

Step 2

Factor $5 m$ out of $15 m^{2} + 10 m$ .

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Step 2.1

Factor $5 m$ out of $15 m^{2}$ .

$\frac{5 m^{2} (m + 1)}{5 m (3 m) + 10 m}$

Step 2.2

Factor $5 m$ out of $10 m$ .

$\frac{5 m^{2} (m + 1)}{5 m (3 m) + 5 m (2)}$

Step 2.3

Factor $5 m$ out of $5 m (3 m) + 5 m (2)$ .

$\frac{5 m^{2} (m + 1)}{5 m (3 m + 2)}$

$\frac{5 m^{2} (m + 1)}{5 m (3 m + 2)}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 m^{2} (m + 1)}{5 m (3 m + 2)}$

Step 3.2

Rewrite the expression.

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

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

Step 4

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

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Step 4.1

Factor $m$ out of $m^{2} (m + 1)$ .

$\frac{m (m (m + 1))}{m (3 m + 2)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Cancel the common factor.

$\frac{m (m (m + 1))}{m (3 m + 2)}$

Step 4.2.2

Rewrite the expression.

$\frac{m (m + 1)}{3 m + 2}$

$\frac{m (m + 1)}{3 m + 2}$

$\frac{m (m + 1)}{3 m + 2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$