Find the domain of the rational function.
-$$r ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 13 x + 36 }$$
A) All real numbers except $- 9$ and $- 4$.
B) All real numbers except 9 and 4 .
C) All real numbers except $- 4$ and 9 .
D) All real numbers except $- 9$ and 4

Question

Quizplus · Accepted Answer

The domain of a rational function is all real numbers except where the denominator equals zero. To find these values, set the denominator equal to zero and solve for $x$: $x^2 - 13x + 36 = 0$. Factoring the quadratic equation gives $(x - 9)(x - 4) = 0$, which means $x = 9$ and $x = 4$ are the values that make the denominator zero. Therefore, the domain is all real numbers except 9 and 4.

Find the Domain of the Rational Function r(x)=x2+x−9x2−13x+36r ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 13 x + 36 }r(x)=x2−13x+36x2+x−9​

Find the Domain of the Rational Function $r ( x ) = \frac { x ^ { 2 } + x - 9 } { x ^ { 2 } - 13 x + 36 }$