Question

simplify 4x^2−12x+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

To simplify the expression \((4x^2−12x+24)/4x\), we can follow the steps you outlined:

1. **Rewrite the polynomial in the denominator as an inverse:**
\[
\frac{4x^2 - 12x + 24}{4x} = (4x^2 - 12x + 24) \cdot \frac{1}{4x}
\]

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

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

Thus, the expression simplifies to:
\[
x - 3 + \frac{6}{x}
\]

4. **Write the final answer in standard form:**
In standard form, it can be presented as:
\[
x - 3 + \frac{6}{x}
\]

Or, if desired, it can be combined into a single expression:
\[
\frac{x^2 - 3x + 6}{x}
\]

Either representation is acceptable, but for clarity, the first option \(x - 3 + \frac{6}{x}\) is a straightforward simplification.