Answer: B is correct.
[tex]\frac{1}{(m-4)(m-3)}[/tex]
Explanation:
Given expression : [tex]\frac{\frac{m+3}{m^2-16}} {\frac{m^2-9}{m+4}}[/tex]
First we write expression into division form.
[tex]\frac{m+3}{m^2-16}\div \frac{m^2-9}{m+4}[/tex]
Change division to multiplication. Expression after division will flip and division sign change to multiply
[tex]\frac{m+3}{m^2-16}\times \frac{m+4}{m^2-9}[/tex] ----------- (A)
Formula: [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]\Rightarrow m^2-16=(m+4)(m-4)[/tex]-------------------------(B)
[tex]\Rightarrow m^2-9=(m+3)(m-3)[/tex]--------------------------(C)
Substitute B and C into A and we get,
[tex]\frac{m+3}{(m+4)(m-4)}\times \frac{m+4}{(m+3)(m-3)}[/tex]
Cancel like factor from top and bottom.
Cancel factors are m+3 and m+4 and we get,
[tex]\frac{1}{(m-4)(m-3)}[/tex]
B is correct.