Basic Math Examples

$\frac{6 y + 9}{3 y - 15} \cdot \frac{y - 5}{4 y + 6}$

Step 1

Factor $3$ out of $6 y + 9$ .

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Step 1.1

Factor $3$ out of $6 y$ .

$\frac{3 (2 y) + 9}{3 y - 15} \cdot \frac{y - 5}{4 y + 6}$

Step 1.2

Factor $3$ out of $9$ .

$\frac{3 (2 y) + 3 (3)}{3 y - 15} \cdot \frac{y - 5}{4 y + 6}$

Step 1.3

Factor $3$ out of $3 (2 y) + 3 (3)$ .

$\frac{3 (2 y + 3)}{3 y - 15} \cdot \frac{y - 5}{4 y + 6}$

Step 2

Factor $3$ out of $3 y - 15$ .

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Step 2.1

Factor $3$ out of $3 y$ .

$\frac{3 (2 y + 3)}{3 (y) - 15} \cdot \frac{y - 5}{4 y + 6}$

Step 2.2

Factor $3$ out of $- 15$ .

$\frac{3 (2 y + 3)}{3 y + 3 \cdot - 5} \cdot \frac{y - 5}{4 y + 6}$

Step 2.3

Factor $3$ out of $3 y + 3 \cdot - 5$ .

$\frac{3 (2 y + 3)}{3 (y - 5)} \cdot \frac{y - 5}{4 y + 6}$

Step 3

Factor $2$ out of $4 y + 6$ .

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Step 3.1

Factor $2$ out of $4 y$ .

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

Step 3.2

Factor $2$ out of $6$ .

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

Step 3.3

Factor $2$ out of $2 (2 y) + 2 (3)$ .

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

Step 4

Cancel the common factor of $2 y + 3$ .

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Step 4.1

Factor $2 y + 3$ out of $3 (2 y + 3)$ .

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

Step 4.2

Factor $2 y + 3$ out of $2 (2 y + 3)$ .

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

Step 4.3

Cancel the common factor.

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

Step 4.4

Rewrite the expression.

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

Step 5

Cancel the common factor of $y - 5$ .

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Step 5.1

Factor $y - 5$ out of $3 (y - 5)$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\frac{3}{3} \cdot \frac{1}{2}$

Step 6

Multiply $\frac{3}{3}$ by $\frac{1}{2}$ .

$\frac{3}{3 \cdot 2}$

Step 7

Multiply $3$ by $2$ .

$\frac{3}{6}$

Step 8

Cancel the common factor of $3$ and $6$ .

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Step 8.1

Factor $3$ out of $3$ .

$\frac{3 (1)}{6}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $6$ .

$\frac{3 \cdot 1}{3 \cdot 2}$

Step 8.2.2

Cancel the common factor.

$\frac{3 \cdot 1}{3 \cdot 2}$

Step 8.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$