Sure, let's simplify the given expression step by step:
We start with the expression:
[tex]\[
\frac{48x^5 - 72x^3 + 44x}{24x^2}
\][/tex]
### Step 1: Break down the expression
Let's separate the fraction across each term in the numerator:
[tex]\[
\frac{48x^5}{24x^2} - \frac{72x^3}{24x^2} + \frac{44x}{24x^2}
\][/tex]
### Step 2: Simplify each term separately
For the first term:
[tex]\[
\frac{48x^5}{24x^2} = \frac{48}{24} \cdot \frac{x^5}{x^2} = 2x^3
\][/tex]
For the second term:
[tex]\[
\frac{72x^3}{24x^2} = \frac{72}{24} \cdot \frac{x^3}{x^2} = 3x
\][/tex]
For the third term:
[tex]\[
\frac{44x}{24x^2} = \frac{44}{24} \cdot \frac{x}{x^2} = \frac{44}{24} \cdot \frac{1}{x} = \frac{11}{6} \cdot \frac{1}{x} = \frac{11}{6x}
\][/tex]
### Step 3: Combine the simplified terms
Putting it all together, we get:
[tex]\[
2x^3 - 3x + \frac{11}{6x}
\][/tex]
So, the simplified form of the expression is:
[tex]\[
2x^3 - 3x + \frac{11}{6x}
\][/tex]
Therefore, the correct answer is:
[tex]\[
2x^3 - 3x + \frac{11}{6x}
\][/tex]
