Divide ((x-4)/(2x^2))÷((2x+3)/(x+4))

$\frac{x - 4}{2 x^{2}} \div \frac{2 x + 3}{x + 4}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 4}{2 x^{2}} \cdot \frac{x + 4}{2 x + 3}$

Multiply $\frac{x - 4}{2 x^{2}}$ by $\frac{x + 4}{2 x + 3}$ .

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

Expand $(x - 4) (x + 4)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Combine the opposite terms in $x \cdot x + x \cdot 4 - 4 x - 4 \cdot 4$ .

Reorder the factors in the terms $x \cdot 4$ and $- 4 x$ .

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

Subtract $4 x$ from $4 x$ .

$\frac{x \cdot x + 0 - 4 \cdot 4}{2 x^{2} (2 x + 3)}$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $- 4$ by $4$ .

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

Split the fraction $\frac{x^{2} - 16}{2 x^{2} (2 x + 3)}$ into two fractions.

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

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2 (2 x + 3)} + \frac{- 16}{2 x^{2} (2 x + 3)}$

Cancel the common factor of $- 16$ and $2$ .

Factor $2$ out of $- 16$ .

$\frac{1}{2 (2 x + 3)} + \frac{2 \cdot - 8}{2 x^{2} (2 x + 3)}$

Cancel the common factors.

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

$\frac{1}{2 (2 x + 3)} + \frac{2 \cdot - 8}{2 (x^{2} (2 x + 3))}$

Cancel the common factor.

$\frac{1}{2 (2 x + 3)} + \frac{2 \cdot - 8}{2 (x^{2} (2 x + 3))}$

Rewrite the expression.

$\frac{1}{2 (2 x + 3)} + \frac{- 8}{x^{2} (2 x + 3)}$

Move the negative in front of the fraction.

$\frac{1}{2 (2 x + 3)} - \frac{8}{x^{2} (2 x + 3)}$