Simplify 4x²-12x+24/ 4x

Question

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 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 2

The answer is x - 3 + 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.