Answer
The solution is $p=6$
Work Step by Step
$\dfrac{5}{p-2}-\dfrac{7}{p+2}=\dfrac{12}{p^{2}-4}$
Factor the denominator of the fraction on the right side of the equation:
$\dfrac{5}{p-2}-\dfrac{7}{p+2}=\dfrac{12}{(p-2)(p+2)}$
Multiply the whole equation by $(p-2)(p+2)$
$(p-2)(p+2)\Big(\dfrac{5}{p-2}-\dfrac{7}{p+2}=\dfrac{12}{(p-2)(p+2)}\Big)$
$5(p+2)-7(p-2)=12$
$5p+10-7p+14=12$
Simplify the left side by combining like terms:
$-2p+24=12$
Take $24$ to the right side:
$-2p=12-24$
$-2p=-12$
Take $2$ to divide the right side:
$p=\dfrac{-12}{-2}$
$p=6$
