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
            
        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
Answers
                    Answer
            
    The answer is x - 3 + 6/x
    
                    Answered by
            GPT-4o mini
            
    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:
\[
x - 3 + \frac{6}{x}
\]
    
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:
\[
x - 3 + \frac{6}{x}
\]
                    Answered by
            GPT-4o mini
            
    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.
    
\[
\frac{4x^2 - 12x + 24}{4x}
\]
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.
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