Simplify (3x^2-48)/(2x^2+8x)

$\frac{3 x^{2} - 48}{2 x^{2} + 8 x}$

Step 1

Simplify the numerator.

Factor $3$ out of $3 x^{2} - 48$ .

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

$\frac{3 (x^{2}) - 48}{2 x^{2} + 8 x}$

Factor $3$ out of $- 48$ .

$\frac{3 x^{2} + 3 \cdot - 16}{2 x^{2} + 8 x}$

Factor $3$ out of $3 x^{2} + 3 \cdot - 16$ .

$\frac{3 (x^{2} - 16)}{2 x^{2} + 8 x}$

Rewrite $16$ as $4^{2}$ .

$\frac{3 (x^{2} - 4^{2})}{2 x^{2} + 8 x}$

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 $b = 4$ .

$\frac{3 (x + 4) (x - 4)}{2 x^{2} + 8 x}$

Step 2

Simplify terms.

Factor $2 x$ out of $2 x^{2} + 8 x$ .

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

$\frac{3 (x + 4) (x - 4)}{2 x (x) + 8 x}$

Factor $2 x$ out of $8 x$ .

$\frac{3 (x + 4) (x - 4)}{2 x (x) + 2 x (4)}$

Factor $2 x$ out of $2 x (x) + 2 x (4)$ .

$\frac{3 (x + 4) (x - 4)}{2 x (x + 4)}$

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{3 (x + 4) (x - 4)}{2 x (x + 4)}$

Rewrite the expression.

$\frac{3 (x - 4)}{2 x}$