Algebra Examples

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

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Rewrite $1$ as $1^{2}$ .

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

Step 1.2

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 $b = 1$ .

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

Step 2

Multiply $\frac{2 y + 3}{(y + 1) (y - 1)} \cdot \frac{1 - y}{y + 1}$ .

Tap for more steps...

Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Add $1$ and $1$ .

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

Step 3

Cancel the common factor of $1 - y$ and $y - 1$ .

Tap for more steps...

Step 3.1

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 3.2

Factor $- 1$ out of $- y$ .

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

Step 3.3

Factor $- 1$ out of $- 1 (- 1) - (y)$ .

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

Step 3.4

Reorder terms.

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

Step 3.5

Cancel the common factor.

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

Step 3.6

Rewrite the expression.

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

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Move $- 1$ to the left of $2 y + 3$ .

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

Step 4.2

Move the negative in front of the fraction.

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