Algebra Examples

$\frac{y - \frac{2}{3}}{y + \frac{1}{5}}$

Step 1

Multiply the numerator and denominator of the fraction by $15$ .

Tap for more steps...

Step 1.1

Multiply $\frac{y - \frac{2}{3}}{y + \frac{1}{5}}$ by $\frac{15}{15}$ .

$\frac{15}{15} \cdot \frac{y - \frac{2}{3}}{y + \frac{1}{5}}$

Step 1.2

Combine.

$\frac{15 (y - \frac{2}{3})}{15 (y + \frac{1}{5})}$

Step 2

Apply the distributive property.

$\frac{15 y + 15 (- \frac{2}{3})}{15 y + 15 (\frac{1}{5})}$

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{15 y + 15 (\frac{- 2}{3})}{15 y + 15 (\frac{1}{5})}$

Step 3.1.2

Factor $3$ out of $15$ .

$\frac{15 y + 3 (5) \frac{- 2}{3}}{15 y + 15 (\frac{1}{5})}$

Step 3.1.3

Cancel the common factor.

$\frac{15 y + 3 \cdot 5 \frac{- 2}{3}}{15 y + 15 (\frac{1}{5})}$

Step 3.1.4

Rewrite the expression.

$\frac{15 y + 5 \cdot - 2}{15 y + 15 (\frac{1}{5})}$

Step 3.2

Multiply $5$ by $- 2$ .

$\frac{15 y - 10}{15 y + 15 (\frac{1}{5})}$

Step 3.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.3.1

Factor $5$ out of $15$ .

$\frac{15 y - 10}{15 y + 5 (3) \frac{1}{5}}$

Step 3.3.2

Cancel the common factor.

$\frac{15 y - 10}{15 y + 5 \cdot 3 \frac{1}{5}}$

Step 3.3.3

Rewrite the expression.

$\frac{15 y - 10}{15 y + 3}$

Step 4

Simplify with factoring out.

Tap for more steps...

Step 4.1

Factor $5$ out of $15 y - 10$ .

Tap for more steps...

Step 4.1.1

Factor $5$ out of $15 y$ .

$\frac{5 (3 y) - 10}{15 y + 3}$

Step 4.1.2

Factor $5$ out of $- 10$ .

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

Step 4.1.3

Factor $5$ out of $5 (3 y) + 5 (- 2)$ .

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

Step 4.2

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

Tap for more steps...

Step 4.2.1

Factor $3$ out of $15 y$ .

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

Step 4.2.2

Factor $3$ out of $3$ .

$\frac{5 (3 y - 2)}{3 (5 y) + 3 (1)}$

Step 4.2.3

Factor $3$ out of $3 (5 y) + 3 (1)$ .

$\frac{5 (3 y - 2)}{3 (5 y + 1)}$