Answer:A
Explanation:
To simplify the rational expression (x²+6x)/(x+5) + (4x+15)/(x+5), we first factor the numerator of the first fraction as x(x+6). Then, we factor the numerator of the second fraction as 4(x+3). Now, we can combine the fractions by finding a common denominator of (x+5) and adding the numerators:
(x²+6x)/(x+5) + (4x+15)/(x+5) = (x(x+6) + 4(x+3))/(x+5)
Simplifying the numerator further, we get:
(x²+6x + 4x + 12)/(x+5) = (x²+10x+12)/(x+5)
Now we can factor the numerator by finding two numbers that multiply to 12 and add to 10. Those numbers are 2 and 6. So we can write:
(x²+10x+12)/(x+5) = (x+2)(x+6)/(x+5)
Therefore, the completely factored and simplified form of the given rational expression is (x+2)(x+6)/(x+5). So the answer is A.