Question

Solve the following inequality:
$\frac{x^2-7x+12}{2x^2+4x+5}>0$

Answer 1

$\frac{x^2-7x+12}{2x^2+4x+5}>0$

As discriminant of$2x^2+4x+5$ is less than $0$.

$\therefore 2x^2+4x+5>0\forall xϵR$

$x^2+7x+12>0$(to hold given equation)

$(x-4)(x-3)>0$

$xϵ(-\infty ,3)\cup (4,\infty )$