Simplify (3y^2-3)/(y^2-1)

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

Step 1

Simplify the numerator.

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

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

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

Factor $3$ out of $- 3$ .

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

Factor $3$ out of $3 (y^{2}) + 3 (- 1)$ .

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

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

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

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 $b = 1$ .

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

Step 2

Simplify the denominator.

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

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

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 $b = 1$ .

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

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $y + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y - 1$ .

Cancel the common factor.

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

Divide $3$ by $1$ .

$3$