\(\frac{96}{x-4}-\frac{120}{x+4}=1\)
\(\Leftrightarrow\frac{96}{x-4}-\frac{120}{x+4}-1=0\)
\(\Leftrightarrow\frac{96\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}-\frac{120\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}-\frac{\left(x-4\right)\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}=0\)
\(\Leftrightarrow\frac{96x+384}{x^2-2^2}-\frac{120x-480}{x^2-2^2}-\frac{x^2-2^2}{x^2-2^2}=0\)
\(\Leftrightarrow\left(96x+384-120x+480-x^2+2^2\right)\cdot\frac{1}{x^2-2^2}=0\)
\(\Leftrightarrow-x^2-24x+868=0\)