Which of the following is a simplified, equivalent form of the rational expression 5x3−8x2+3/4x2 ?(1 point) Responses 5x^3/4−2x^2+3/4x^2

Question

5x/4−2+3/4x^2
5x/4+3/4x^2
5x^5/4−2x^4+3/4x^2

Answer 1

To simplify the rational expression \(\frac{5x^3 - 8x^2 + 3}{4x^2}\), we can separate the fraction as follows:

\[ \frac{5x^3}{4x^2} - \frac{8x^2}{4x^2} + \frac{3}{4x^2} \]

Now, let's simplify each term:

1. \(\frac{5x^3}{4x^2} = \frac{5}{4} x^{3-2} = \frac{5}{4} x\)

2. \(\frac{8x^2}{4x^2} = 2\)

3. \(\frac{3}{4x^2}\) remains as is.

Putting it all together, we get:

\[ \frac{5}{4}x - 2 + \frac{3}{4x^2} \]

So the simplified expression is:

\[ \frac{5}{4}x - 2 + \frac{3}{4x^2} \]

Looking at the provided responses, the equivalent simplified form is:

5x/4 - 2 + 3/4x^2.