Question

Find the domain of definition of the following function.
$y=\sqrt{\frac{x^2-5x+12}{x^2+6x+8}}.$

Answer 1

$f\left(x\right)=\sqrt{\frac{x^2-5x+12}{x^2+6x+8}}$

for $h\left(x\right)=x^2-5x+12D<0$

for $g\left(x\right)=x^2+6x+8$

$g\left(x\right)=(x+2)(x+4)>0$

$xϵ(-\infty ,-4)\cup (-2,\infty )$

so, domain of $f\left(x\right)$ is

$xϵ(-\infty ,-4)\cup (-2,\infty )$