\(x ( x \,- 1 ) \,- \dfrac{ x \,- 1 }{x} > 0\)
\(\dfrac{x^2( x \,- 1 ) - ( x \,- 1 )}{x} > 0\)
\(\dfrac{( x^2 \,- 1 ) ( x \,- 1 )}{x} > 0\)
\(\dfrac{( x + 1 ) ( x \,- 1 )^2}{x} > 0\)
So the critical numbers are \(-1, 1\) and \(0\). The critical numbers \(-1\) and \(0\) are transitive and \(1\) is intransitive. The ratio of the leading coefficients is positive, so the expression is positive on the right-most interval \(( 1, \infty )\). The sign doesn’t change at the intransitive critical number \(1\), so the expression is also positive on the interval \(( 0, 1 )\). The sign changes at the transitive critical number \(0\), so the expression is negative on the interval \(( -1, 0 )\). The sign changes at the transitive critical number \(-1\), so the expression is positive on the interval \(( -\infty, -1 )\). Thus the solution is \(( -\infty, -1 ) \cup ( 0, 1 ) \cup ( 1, \infty )\)