Basic Math Examples

$\frac{y}{6 y - 30} \cdot \frac{y^{2} - 5 y}{9}$

Step 1

Factor $6$ out of $6 y - 30$ .

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Step 1.1

Factor $6$ out of $6 y$ .

$\frac{y}{6 (y) - 30} \cdot \frac{y^{2} - 5 y}{9}$

Step 1.2

Factor $6$ out of $- 30$ .

$\frac{y}{6 y + 6 \cdot - 5} \cdot \frac{y^{2} - 5 y}{9}$

Step 1.3

Factor $6$ out of $6 y + 6 \cdot - 5$ .

$\frac{y}{6 (y - 5)} \cdot \frac{y^{2} - 5 y}{9}$

Step 2

Factor $y$ out of $y^{2} - 5 y$ .

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Step 2.1

Factor $y$ out of $y^{2}$ .

$\frac{y}{6 (y - 5)} \cdot \frac{y \cdot y - 5 y}{9}$

Step 2.2

Factor $y$ out of $- 5 y$ .

$\frac{y}{6 (y - 5)} \cdot \frac{y \cdot y + y \cdot - 5}{9}$

Step 2.3

Factor $y$ out of $y \cdot y + y \cdot - 5$ .

$\frac{y}{6 (y - 5)} \cdot \frac{y (y - 5)}{9}$

Step 3

Cancel the common factor of $y - 5$ .

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Step 3.1

Factor $y - 5$ out of $6 (y - 5)$ .

$\frac{y}{(y - 5) \cdot 6} \cdot \frac{y (y - 5)}{9}$

Step 3.2

Factor $y - 5$ out of $y (y - 5)$ .

$\frac{y}{(y - 5) \cdot 6} \cdot \frac{(y - 5) y}{9}$

Step 3.3

Cancel the common factor.

$\frac{y}{(y - 5) \cdot 6} \cdot \frac{(y - 5) y}{9}$

Step 3.4

Rewrite the expression.

$\frac{y}{6} \cdot \frac{y}{9}$

Step 4

Multiply $\frac{y}{6}$ by $\frac{y}{9}$ .

$\frac{y \cdot y}{6 \cdot 9}$

Step 5

Raise $y$ to the power of $1$ .

$\frac{y^{1} y}{6 \cdot 9}$

Step 6

Raise $y$ to the power of $1$ .

$\frac{y^{1} y^{1}}{6 \cdot 9}$

Step 7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{y^{1 + 1}}{6 \cdot 9}$

Step 8

Add $1$ and $1$ .

$\frac{y^{2}}{6 \cdot 9}$

Step 9

Multiply $6$ by $9$ .

$\frac{y^{2}}{54}$