Basic Math Examples

$\frac{3 m}{m + 2 y} \cdot \frac{10 m y + 5 m^{2}}{6 m}$

Step 1

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

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Step 1.1

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

$\frac{3 m}{m + 2 y} \cdot \frac{5 m (2 y) + 5 m^{2}}{6 m}$

Step 1.2

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

$\frac{3 m}{m + 2 y} \cdot \frac{5 m (2 y) + 5 m (m)}{6 m}$

Step 1.3

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

$\frac{3 m}{m + 2 y} \cdot \frac{5 m (2 y + m)}{6 m}$

Step 2

Cancel the common factor of $3 m$ .

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Step 2.1

Factor $3 m$ out of $6 m$ .

$\frac{3 m}{m + 2 y} \cdot \frac{5 m (2 y + m)}{3 m (2)}$

Step 2.2

Cancel the common factor.

$\frac{3 m}{m + 2 y} \cdot \frac{5 m (2 y + m)}{3 m \cdot 2}$

Step 2.3

Rewrite the expression.

$\frac{1}{m + 2 y} \cdot \frac{5 m (2 y + m)}{2}$

Step 3

Multiply $\frac{1}{m + 2 y}$ by $\frac{5 m (2 y + m)}{2}$ .

$\frac{5 m (2 y + m)}{(m + 2 y) \cdot 2}$

Step 4

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

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Step 4.1

Reorder terms.

$\frac{5 m (m + 2 y)}{(m + 2 y) \cdot 2}$

Step 4.2

Cancel the common factor.

$\frac{5 m (m + 2 y)}{(m + 2 y) \cdot 2}$

Step 4.3

Rewrite the expression.

$\frac{5 m}{2}$