Find the indicated function and write its domain in interval notation.
-$$s ( x ) = \frac { x - 4 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 4 - x } , \left( \frac { s } { t } \right) ( x ) = ?$$
A) $- \frac { ( x - 4 ) ^ { 2 } } { ( x - 6 ) ^ { 2 } ( x + 6 ) } ; ( - \infty , - 6 ) \cup ( - 6,4 ) \cup ( 4,6 ) \cup ( 6 , \infty )$
B) $- \frac { 1 } { x + 6 } ; ( - \infty , - 6 ) \cup ( - 6 , \infty )$
C) $- \frac { ( x - 4 ) ^ { 2 } } { ( x - 6 ) ^ { 2 } ( x + 6 ) } ; ( - \infty , - 6 ) \cup ( 6 , \infty )$
D) $- \frac { 1 } { x + 6 } ; ( - \infty , - 6 ) \cup ( - 6,4 ) \cup ( 4,6 ) \cup ( 6 , \infty )$

Question

Quizplus · Accepted Answer

The division of $s(x)$ by $t(x)$ simplifies to $- \frac { ( x - 4 ) ^ { 2 } } { ( x - 6 ) ^ { 2 } ( x + 6 ) }$. The domain excludes the values where the denominator is zero, which are $x = -6, 6$, and the simplification process removes the restriction at $x = 4$, hence the domain is $( - \infty , - 6 ) \cup ( - 6,4 ) \cup ( 4,6 ) \cup ( 6 , \infty )$.

Find the Indicated Function and Write Its Domain in Interval s(x)=x−4x2−36,t(x)=x−64−x,(st)(x)=?s ( x ) = \frac { x - 4 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 4 - x } , \left( \frac { s } { t } \right) ( x ) = ?s(x)=x2−36x−4​,t(x)=4−xx−6​,(ts​)(x)=?

Find the Indicated Function and Write Its Domain in Interval $s ( x ) = \frac { x - 4 } { x ^ { 2 } - 36 } , t ( x ) = \frac { x - 6 } { 4 - x } , \left( \frac { s } { t } \right) ( x ) = ?$