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.