Simplify (3p-4)/(p^2-4)-(3p-6)/(p^2-4)

$\frac{3 p - 4}{p^{2} - 4} - \frac{3 p - 6}{p^{2} - 4}$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{3 p - 4 - (3 p - 6)}{p^{2} - 4}$

Simplify each term.

Apply the distributive property.

$\frac{3 p - 4 - (3 p) - - 6}{p^{2} - 4}$

Multiply $3$ by $- 1$ .

$\frac{3 p - 4 - 3 p - - 6}{p^{2} - 4}$

Multiply $- 1$ by $- 6$ .

$\frac{3 p - 4 - 3 p + 6}{p^{2} - 4}$

Simplify by adding terms.

Combine the opposite terms in $3 p - 4 - 3 p + 6$ .

Subtract $3 p$ from $3 p$ .

$\frac{0 - 4 + 6}{p^{2} - 4}$

Subtract $4$ from $0$ .

$\frac{- 4 + 6}{p^{2} - 4}$

Add $- 4$ and $6$ .

$\frac{2}{p^{2} - 4}$

Simplify the denominator.

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

$\frac{2}{p^{2} - 2^{2}}$

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

$\frac{2}{(p + 2) (p - 2)}$