Final Answer:
The quotient of (x+5) divided by √(4x²+25x+12) simplifies to (x+5)/(2x+3). Thus the correct option is B.
Step-by-step explanation:
To find the quotient of (x+5) divided by √(4x²+25x+12), it's beneficial to factorize the denominator to simplify the expression. Factoring 4x²+25x+12 gives us (2x+3)(2x+4). The square root of this expression simplifies to 2x+3. Therefore, the division becomes (x+5)/(2x+3). This quotient represents the simplest form of the given expression.
Breaking down the process, the denominator √(4x²+25x+12) is factorized to (2x+3)(2x+4), allowing us to rewrite the expression as (x+5)/(2x+3). This form represents the quotient, showing the result after simplification.
Therefore, the correct answer is a) (x+5)/(2x+3). This simplification indicates that when dividing (x+5) by the square root of (4x²+25x+12), the resulting quotient is (x+5)/(2x+3). Thus the correct option is B.