Find the domain of the following rational function. H(x)=(13x^2+x)/(x^2)+4 Select the correct choice below and , if necessary, fill in the answer box to c A. The domain of H(x) is restricted to square (Type your answer in interval notation.) B. There are no restrictions on the domain of H(x)

To find the domain of the rational function \( H(x) = \frac{13x^2 + x}{x^2 + 4} \), we need to determine where the denominator is not equal to zero, since division by zero is undefined.<br /><br />The denominator of the function is \( x^2 + 4 \). We set this equal to zero and solve for \( x \):<br /><br />\[<br />x^2 + 4 = 0<br />\]<br /><br />Subtract 4 from both sides:<br /><br />\[<br />x^2 = -4<br />\]<br /><br />Since there are no real numbers whose square is negative, \( x^2 = -4 \) has no real solutions. Therefore, the denominator \( x^2 + 4 \) is never zero for any real number \( x \).<br /><br />This means that there are no restrictions on the domain of \( H(x) \) in terms of real numbers. The function is defined for all real values of \( x \).<br /><br />Thus, the correct choice is:<br /><br />B. There are no restrictions on the domain of \( H(x) \).