simplify: 30 /m^2-25 + 3 /m+5?

Question

a. 3m+25 /m^2-25
b. 33 /m^2-25
c. 3 /m-5
d. 3(m+15) /(m+5)(m-5)

Answer 1

(30/m^2-25)+(3/m+5)
={30/(m+5)(m-5)}+ (3/m+5)
={30+3(m-5)}/{(m+5)(m-5)}
=(30+3m-15)/(m+5)(m-5)
=(3m+15)/(m+5)(m-5)
=3(m+5)/(m+5)(m-5)
=3/(m-5) [after cancelling (m+5 from both numerator and denominator]
Hence c is correct

Answer 2

I assume the problem is
30/(m^2 - 25) + 3/(m+5)

that being the case, m^2-25 is the difference of two squares, so it factors to (m+5)(m-5). The LCD then is (m^2-25) Multiply the 2nd fraction by (m-5)/(m-5) (which is 1, so doens't change the value) to get

30/(m^2-25) + (3m-15)/(m^2-25)
= (30 + 3m - 15)/(m^2 - 25)
= (3m+15)/(m^2-25)
= 3(m+5)/(m-5)(m+5)
= 3/(m-5)

So your answer is c.