Basic Math Examples

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

Step 1

To write $\frac{y}{y + 2}$ as a fraction with a common denominator, multiply by $\frac{y - 3}{y - 3}$ .

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

Step 2

Write each expression with a common denominator of $(y - 3) (y + 2)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

Reorder the factors of $(y - 3) (y + 2)$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Apply the distributive property.

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

Step 4.2

Multiply $y$ by $y$ .

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

Step 4.3

Move $- 3$ to the left of $y$ .

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

Step 4.4

Subtract $3 y$ from $3 y$ .

$\frac{- 4 + y^{2} + 0}{(y + 2) (y - 3)}$

Step 4.5

Add $- 4 + y^{2}$ and $0$ .

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

Step 4.6

Rewrite $- 4 + y^{2}$ in a factored form.

Tap for more steps...

Step 4.6.1

Rewrite $4$ as $2^{2}$ .

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

Step 4.6.2

Reorder $- 2^{2}$ and $y^{2}$ .

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

Step 4.6.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 2$ .

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

Step 5

Cancel the common factor of $y + 2$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$\frac{y - 2}{y - 3}$