Simplify:
(2x+3)^3/2 + (2x+3)^-1/2 /
2x+3
Can anyone explain how to work it out please? Thanks
To simplify the given expression ((2x+3)^(3/2) + (2x+3)^(-1/2)) / (2x+3), you can follow these steps:
Step 1: Simplify the numerator first.
The numerator contains two terms: (2x+3)^(3/2) and (2x+3)^(-1/2).
Let's start with the first term: (2x+3)^(3/2).
To simplify this term, you can rewrite it as the square root of (2x+3) raised to the power of 3.
(2x+3)^(3/2) = √(2x+3)^3
Now, let's move on to the second term: (2x+3)^(-1/2).
To simplify this term, you can take the reciprocal of the square root of (2x+3).
(2x+3)^(-1/2) = 1 / √(2x+3)
The numerator can now be simplified as follows:
((2x+3)^(3/2) + (2x+3)^(-1/2)) = √(2x+3)^3 + 1 / √(2x+3)
Step 2: Simplify the denominator.
The denominator is simply 2x+3.
Step 3: Combine the simplified numerator and denominator.
Now that the numerator and denominator have been simplified, you can combine them to get the final simplified expression:
((2x+3)^(3/2) + (2x+3)^(-1/2)) / (2x+3) =
(√(2x+3)^3 + 1 / √(2x+3)) / (2x+3)
That is the simplified form of the given expression.