ANSWER:
B. x = 10
C. x = -10
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\frac{5x}{4x+40}+\frac{x+100}{6}=\frac{30}{x^2-100}[/tex]
To determine the domain, we must know that it is the set of input values of a function, in this case they would be the values that x can take.
Because it is a rational equation, the denominator cannot be equal to 0, therefore, we set the corresponding denominators equal to 0 as follows:
[tex]\begin{gathered} 4x+40=0 \\ \\ \text{ we solve for x:} \\ \\ 4x=-40 \\ \\ x=\frac{-40}{4}=-10 \\ \\ \\ x^2-100=0 \\ \\ x^2=100 \\ \\ x=\sqrt{100} \\ \\ x=\pm10 \end{gathered}[/tex]
This means that the domain is equal to all the real ones except when x is equal to 10 and -10, that is, those would be the restrictions of the domain.
Therefore, the correct answer is B. x = 10 and C. x = -10
