Set of all real values of x satisfying the in equation _ 2 (x^ 2 -...

$\dfrac{\log_{2}\left(x^{2} - 5x + 4\right)}{\log_{2} \left(x^{2} + 1\right)} > 1$

x^{2} - 5x + 4 > 0 ⇒ \left(x - 4\right)\left(x - 1\right) > 0$</p><p>$⇒ x \in \left(- \infty ,1\right) \cup \left(4, \infty\right) . . . \left(1\right)$</p><p>$x^{2} + 1 > 0$~which is true~$\forall x \in \mathbb{R} . . . \left(2\right)

$\log_{2} \left(x^{2} - 5x + 4\right) > \log_{2} \left(x^{2} + 1\right)$

$x^{2} - 5x + 4 > x^{2} + 1$

$- 5x + 3 > 0$

x < \dfrac{3}{5} . . . \left(3\right)$</p><p>From equations, \left(1\right), \left(2\right)$ and \left(3\right)~we get

x \in \left(- \infty ,\dfrac{3}{5}\right) - \left\{0\right\}$</p>$