Find the domain of the rational function. $h ( x ) = \frac { 6 x } { x ^ { 2 } + 4 }$
A) $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$
B) $( - \infty , \infty )$
C) $( - \infty , 6 ) \cup ( 6 , \infty )$
D) $( - \infty , 2 ) \cup ( 2,6 ) \cup ( 6 , \infty )$
E) $( - \infty , 0 ) \cup ( 0 , \infty )$

Question

Quizplus · Accepted Answer

The denominator $x^2 + 4$ is never zero for any real value of $x$, because $x^2$ is always non-negative, making $x^2 + 4 > 0$ for all real $x$. Therefore, the domain is all real numbers.

Find the Domain of the Rational Function h(x)=6xx2+4h ( x ) = \frac { 6 x } { x ^ { 2 } + 4 }h(x)=x2+46x​

Find the Domain of the Rational Function $h ( x ) = \frac { 6 x } { x ^ { 2 } + 4 }$