Add.
start fraction a over a plus 3 end fraction plus start fraction a plus 5 over 4 end fraction
A. start fraction 4 a plus 20 over left parenthesis a plus 3 right parenthesis times left parenthesis a plus 5 right parenthesis end fraction
B. start fraction a squared plus 12 a plus 15 over 4 times left parenthesis a plus 3 right parenthesis end fraction
C. start fraction a squared plus 19 a plus 8 over 4 times left parenthesis a plus 3 right parenthesis end fraction
D. start fraction 4 a squared plus 19 a plus 8 over 4 left parenthesis a plus 3 right parenthesis end fraction
The answer is B.
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 4(a+3):
start fraction a over a+3 end fraction + start fraction a+5 over 4 = start fraction 4a over 4(a+3) end fraction + start fraction a+3(a+3) over 4(a+3) end fraction
Now we can combine the numerators:
start fraction 4a + a(a+3) + 5(a+3) over 4(a+3) end fraction
Simplifying the expression:
start fraction a^2 + 12a + 15 over 4(a+3) end fraction
Therefore, the answer is B.