Algebra Examples

$\frac{3 y + 2}{3 y} \div \frac{6 y^{2} + 4 y}{3 y + 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 y + 2}{3 y} \cdot \frac{3 y + 2}{6 y^{2} + 4 y}$

Step 2

Factor $2 y$ out of $6 y^{2} + 4 y$ .

Tap for more steps...

Step 2.1

Factor $2 y$ out of $6 y^{2}$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

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

$\frac{3 y + 2}{3 y (2 y)}$

Step 5

Multiply $2$ by $3$ .

$\frac{3 y + 2}{6 y \cdot y}$

Step 6

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

$\frac{3 y + 2}{6 (y^{1} y)}$

Step 7

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

$\frac{3 y + 2}{6 (y^{1} y^{1})}$

Step 8

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

$\frac{3 y + 2}{6 y^{1 + 1}}$

Step 9

Add $1$ and $1$ .

$\frac{3 y + 2}{6 y^{2}}$

Step 10

Split the fraction $\frac{3 y + 2}{6 y^{2}}$ into two fractions.

$\frac{3 y}{6 y^{2}} + \frac{2}{6 y^{2}}$

Step 11

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

Tap for more steps...

Step 11.1

Factor $3$ out of $3 y$ .

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

Step 11.2

Cancel the common factors.

Tap for more steps...

Step 11.2.1

Factor $3$ out of $6 y^{2}$ .

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

Step 11.2.2

Cancel the common factor.

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

Step 11.2.3

Rewrite the expression.

$\frac{y}{2 y^{2}} + \frac{2}{6 y^{2}}$

Step 12

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

Tap for more steps...

Step 12.1

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

$\frac{y^{1}}{2 y^{2}} + \frac{2}{6 y^{2}}$

Step 12.2

Factor $y$ out of $y^{1}$ .

$\frac{y \cdot 1}{2 y^{2}} + \frac{2}{6 y^{2}}$

Step 12.3

Cancel the common factors.

Tap for more steps...

Step 12.3.1

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

$\frac{y \cdot 1}{y (2 y)} + \frac{2}{6 y^{2}}$

Step 12.3.2

Cancel the common factor.

$\frac{y \cdot 1}{y (2 y)} + \frac{2}{6 y^{2}}$

Step 12.3.3

Rewrite the expression.

$\frac{1}{2 y} + \frac{2}{6 y^{2}}$

Step 13

Cancel the common factor of $2$ and $6$ .

Tap for more steps...

Step 13.1

Factor $2$ out of $2$ .

$\frac{1}{2 y} + \frac{2 (1)}{6 y^{2}}$

Step 13.2

Cancel the common factors.

Tap for more steps...

Step 13.2.1

Factor $2$ out of $6 y^{2}$ .

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

Step 13.2.2

Cancel the common factor.

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

Step 13.2.3

Rewrite the expression.

$\frac{1}{2 y} + \frac{1}{3 y^{2}}$