Simplify (5x^2-5)/(3x^2+3x)

$\frac{5 x^{2} - 5}{3 x^{2} + 3 x}$

Step 1

Simplify the numerator.

Factor $5$ out of $5 x^{2} - 5$ .

Factor $5$ out of $5 x^{2}$ .

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

Factor $5$ out of $- 5$ .

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

Factor $5$ out of $5 (x^{2}) + 5 (- 1)$ .

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

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

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

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 $b = 1$ .

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

Step 2

Simplify terms.

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

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

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

Factor $3 x$ out of $3 x$ .

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

Factor $3 x$ out of $3 x (x) + 3 x (1)$ .

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

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 (x - 1)}{3 x}$