Question

Solve the following inequality:
$\frac{5x^2-2}{4x^2-x+3}<1$

Answer 1

$\frac{5x^2-2}{4x^2-x+3}<1$

$\frac{5x^2-2}{4x^2-x+3}-1<0$

$\frac{5x^2-2-4x^2+x-3}{4x^2-x+3}<0$

$\frac{x^2+x-5}{4x^2-x+3}<0$

$(4x^2-x+3=(2x-\frac{1}{4}{)}^2+\frac{47}{16}>0$

$x^2+x-5<0⟹x\in (\frac{-1-\sqrt{21}}{2},\frac{-1+\sqrt{21}}{2})$