Question

Simplify 4x²-12x+24/ 4x
Write your answer in standard form.

Rewrite the polynomial in the denominator as an inverse term and distribute it to each term of the numerator, then simplify

Answer 1

The answer is x - 3 + 6/x

Answer 2

To simplify the expression \((4x^2 - 12x + 24) / (4x)\), we can rewrite the denominator as an inverse term and then distribute it to each term of the numerator.

1. Rewrite the expression:
\[
\frac{4x^2 - 12x + 24}{4x} = \left(4x^2 - 12x + 24\right) \cdot \frac{1}{4x}
\]

2. Distribute \(\frac{1}{4x}\) to each term in the numerator:
\[
= \frac{4x^2}{4x} - \frac{12x}{4x} + \frac{24}{4x}
\]

3. Simplifying each term:
- For the first term:
\[
\frac{4x^2}{4x} = x
\]
- For the second term:
\[
-\frac{12x}{4x} = -3
\]
- For the third term:
\[
\frac{24}{4x} = \frac{6}{x}
\]

4. Combine all the simplified terms:
\[
x - 3 + \frac{6}{x}
\]

5. Writing the final answer in standard form:
\[
x - 3 + \frac{6}{x} \quad \text{(This is the simplified expression.)}
\]

In a more standard polynomial form, it can be written as:
\[
x - 3 + 6x^{-1}
\]

Thus, the simplified form of the original expression is:
\[
x - 3 + \frac{6}{x}
\]

Answer 3

Yes, you are correct! The simplified form of the expression

\[
\frac{4x^2 - 12x + 24}{4x}
\]

is indeed

\[
x - 3 + \frac{6}{x}.
\]

To recap the steps:

1. Rewrite the expression as

\[
\frac{4x^2}{4x} - \frac{12x}{4x} + \frac{24}{4x}.
\]

2. Simplify each term:

- \(\frac{4x^2}{4x} = x\)
- \(-\frac{12x}{4x} = -3\)
- \(\frac{24}{4x} = \frac{6}{x}\)

3. Combine the simplified terms to get:

\[
x - 3 + \frac{6}{x}
\]

So your answer \(x - 3 + \frac{6}{x}\) is indeed correct! Thank you for your input.