Simplify (3x^2-3)/((x+1)(x-3))

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

Step 1

Simplify the numerator.

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

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

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

Factor $3$ out of $- 3$ .

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

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

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

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

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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

Step 2

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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