Calculus with Applications (10th Edition)

The solution is $p=6$
$\dfrac{5}{p-2}-\dfrac{7}{p+2}=\dfrac{12}{p^{2}-4}$ 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: $p=\dfrac{-12}{-2}$ $p=6$