Answer
$\dfrac{5x^2-2}{(x-1)^2}$
Work Step by Step
Factoring the expressions and cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{5x^4+3x^2-2}{x-1}\cdot\dfrac{x+1}{x^4-1}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(5x^2-2)(x^2+1)}{x-1}\cdot\dfrac{x+1}{(x^2+1)(x^2-1)}
\\\\=
\dfrac{(5x^2-2)(x^2+1)}{x-1}\cdot\dfrac{x+1}{(x^2+1)(x+1)(x-1)}
\\\\=
\dfrac{(5x^2-2)(\cancel{x^2+1})}{x-1}\cdot\dfrac{\cancel{x+1}}{(\cancel{x^2+1})(\cancel{x+1})(x-1)}
\\\\=
\dfrac{5x^2-2}{(x-1)^2}
.\end{array}
