Question

The value of $x$ satisfying the inequation $\frac{x^2-7x+12}{2x^2+4x+5}>0$ is

• A. $(3,4)$
• B. $(2,4)$
• C. $(-\infty ,3)\cup (4,\infty )$
• D. All real numbers

Answer 1

The correct option is C $(-\infty ,3)\cup (4,\infty )$

$2x^2+4x+5$ is always positive as $D=b^2-4ac=16-40=-24$

$\frac{(x-4)(x-3)}{x^2+4x+5}>0$

Clearly for this equation to be positive $x>4$ or $x<3$ as suggested in option C.