Question

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

A. 9/(m-9)(m+9)
B. 4m+41/(m-9)(m+9)
C.9/m2+m-72
D.4m-31/(m-9)(m+9)

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

Step-by-step explanation:
1- The given expression is:

`(4)/(m+9)` +
`(5)/(m^2 - 81)`

2- Factorize the denominator of the second term:

`(4)/(m+9)` +
`(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):

`(4(m-9))/((m-9)(m+9))` +
`(5)/((m-9)(m+9))`

This will give:

`(4m-36)/((m+9)(m-9))` +
`(5)/((m-9)(m+9))`

4- Add the numerators normally since the two terms have common denominator:

`(4m-36+5)/((m-9)(m+9))` =
`(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 :)