Answer:
[tex]\frac{1}{(m-3)(m-4)}[/tex]
Step-by-step explanation:
(m+3/m^2-16)/(m^2-9/m+4)
Lets factor the numerator and denominator
use identity a^2 - b^2 = (a+b)(a-b)
[tex]m^2 - 16= m^2 - 4^2 = (m+4)(m-4)[/tex]
[tex]m^2 - 9= m^2 - 3^2 = (m+3)(m-3)[/tex]
we have divisiion sign in between, change the division symbol in to multiplication symbol by flipping the fraction in the denominator
(m+3/m^2-16)*(m+4/m^2-9)
[tex]\frac{m+3}{(m+4)(m-4)} * \frac{m+4}{(m+3)(m-3)}[/tex]
Cancel put m+3 and m+4 at the top and botom
[tex]\frac{1}{(m-3)(m-4)}[/tex]
