Question

Simplify the sum 4/m+9+5/m^2-81

Answer 1

   4/(m+9)+5/(m^2-81)= 
  4/ ( m+9) +5 / ( m-9)(m+9)=
4(m-9)/(m+9)(m-9)+ 5 / (m+9)(m-9)=
(4m-36+5)/(m+9)(m-9)=
4m-31/ (m+9)(m-9)

the answer is D

Answer 2

Answer:
D

Explanation:
1- The given expression is:
$\frac{4}{m+9}$ + $\frac{5}{m^2 - 81}$

2- Factorize the denominator of the second term:
$\frac{4}{m+9}$ + $\frac{5}{(m+9)(m-9)}$

3- Get the common denominator for both terms. In this case, the common denominator would be (m+9)(m-9):
$\frac{4(m-9)}{(m-9)(m+9)}$ + $\frac{5}{(m-9)(m+9)}$

This will give:
$\frac{4m-36}{(m+9)(m-9)}$ + $\frac{5}{(m-9)(m+9)}$

4- Add the numerators normally since the two terms have common denominator:
$\frac{4m-36+5}{(m-9)(m+9)}$ = $\frac{4m-31}{(m-9)(m+9)}$

Comparing the calculated result with the given options, we will find that the correct option is the last one

Hope this helps :)