Answer:
D
Explanation:
1- The given expression is:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{m^2 - 81} [/tex]
2- Factorize the denominator of the second term:
[tex] \frac{4}{m+9} [/tex] + [tex] \frac{5}{(m+9)(m-9)} [/tex]
3- Get the common denominator for both terms. In this case, the common denominator would be (m+9)(m-9):
[tex] \frac{4(m-9)}{(m-9)(m+9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]
This will give:
[tex] \frac{4m-36}{(m+9)(m-9)} [/tex] + [tex] \frac{5}{(m-9)(m+9)} [/tex]
4- Add the numerators normally since the two terms have common denominator:
[tex] \frac{4m-36+5}{(m-9)(m+9)} [/tex] = [tex] \frac{4m-31}{(m-9)(m+9)} [/tex]
Comparing the calculated result with the given options, we will find that the correct option is the last one
Hope this helps :)
