Answer
$\frac{dy}{dx}$ = [$\frac{2x^{2}+4}{x^{4}-5x^{2}+4}$ ][$\frac{(x+1)(x-2)}{(x-1)(x+2)}$]
Work Step by Step
$y$ = $\frac{(x+1)(x-2)}{(x-1)(x+2)}$
$apply$ $\ln()$ $on$ $both$ $side$
$\ln$$y$ = $\ln$$(x+1)$ + $\ln$$(x-2)$ - $\ln$$(x-1)$ - $\ln$$(x+2)$
$\frac{1}{y}$ $\frac{dy}{dx}$ = $\frac{1}{x+1}$ + $\frac{1}{x-2}$ - $\frac{1}{x-1}$ - $\frac{1}{x+2}$
$\frac{1}{y}$ $\frac{dy}{dx}$ = [$\frac{1}{x+1}$ - $\frac{1}{x-1}$] +[$\frac{1}{x-2}$ - $\frac{1}{x+2}$ ]
$\frac{1}{y}$ $\frac{dy}{dx}$ = [$\frac{x-1-x-1}{x^{2}-1}$] + [$\frac{x+2-x+2}{x^{2}-4}$]
$\frac{1}{y}$ $\frac{dy}{dx}$ = $\frac{-2}{x^{2}-1}$ + $\frac{4}{x^{2}-4}$
$\frac{1}{y}$ $\frac{dy}{dx}$ = $\frac{-2x^{2}+8+4x^{2}-4}{x^{4}-5x^{2}+4}$
$\frac{1}{y}$ $\frac{dy}{dx}$ = $\frac{2x^{2}+4}{x^{4}-5x^{2}+4}$
$\frac{dy}{dx}$ = $\frac{2x^{2}+4}{x^{4}-5x^{2}+4}$ $(y)$
$\frac{dy}{dx}$ = [$\frac{2x^{2}+4}{x^{4}-5x^{2}+4}$ ][$\frac{(x+1)(x-2)}{(x-1)(x+2)}$]
