Answer: Second option
Step-by-step explanation:
You need to make the multiplication of the function [tex]c(x)=\frac{5}{x-2}[/tex] and the function [tex]d(x)=x+3[/tex]. Then:
[tex](cd)(x)=(\frac{5}{x-2})(x+3)[/tex]
You need to apply the Distributive property:
[tex](cd)(x)=\frac{5(x+3)}{x-2}\\\\(cd)(x)=\frac{5x+15}{x-2}[/tex]
Therefore, the domain will be all the number that make the denominator equal to zero.
Then, make the denominator equal to zero and solve for x:
[tex]x-2=0\\x=2[/tex]
Therefore, the domain is: All real values of x except [tex]x=2[/tex]
