Simplify (6x^2-54)/(5x^2+15x)

$\frac{6 x^{2} - 54}{5 x^{2} + 15 x}$

Step 1

Simplify the numerator.

Factor $6$ out of $6 x^{2} - 54$ .

Factor $6$ out of $6 x^{2}$ .

$\frac{6 (x^{2}) - 54}{5 x^{2} + 15 x}$

Factor $6$ out of $- 54$ .

$\frac{6 x^{2} + 6 \cdot - 9}{5 x^{2} + 15 x}$

Factor $6$ out of $6 x^{2} + 6 \cdot - 9$ .

$\frac{6 (x^{2} - 9)}{5 x^{2} + 15 x}$

Rewrite $9$ as $3^{2}$ .

$\frac{6 (x^{2} - 3^{2})}{5 x^{2} + 15 x}$

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 $b = 3$ .

$\frac{6 (x + 3) (x - 3)}{5 x^{2} + 15 x}$

Step 2

Simplify terms.

Factor $5 x$ out of $5 x^{2} + 15 x$ .

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

$\frac{6 (x + 3) (x - 3)}{5 x (x) + 15 x}$

Factor $5 x$ out of $15 x$ .

$\frac{6 (x + 3) (x - 3)}{5 x (x) + 5 x (3)}$

Factor $5 x$ out of $5 x (x) + 5 x (3)$ .

$\frac{6 (x + 3) (x - 3)}{5 x (x + 3)}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{6 (x + 3) (x - 3)}{5 x (x + 3)}$

Rewrite the expression.

$\frac{6 (x - 3)}{5 x}$