Find the domain of the rational function. $h(t)=\frac{10t^2}{t^2-4t-45}$

A) $(-\infty ,0)\cup (0,\infty )$
B) $(-\infty ,\infty )$
C) $(-\infty ,-5)\cup (-5,0)\cup (0,\infty )$
D) $(-\infty ,0)\cup (0,9)\cup (9,\infty )$
E) $(-\infty ,-5)\cup (-5,9)\cup (9,\infty )$

The domain of a rational function is all real numbers except where the denominator equals zero. To find these points for $h(t)=\frac{10t^2}{t^2-4t-45}$ , set the denominator equal to zero and solve for $t$ : $t^2-4t-45=0$ . Factoring the quadratic equation gives $(t-9)(t+5)=0$ , so $t=9$ and $t=-5$ are the points where the function is undefined. Thus, the domain is all real numbers except $t=9$ and $t=-5$ , which corresponds to $(-\infty ,-5)\cup (-5,9)\cup (9,\infty )$ .