Question

Simplify \frac{4x^2-12x+24}{4x}. Write your answer in standard form

Answer 1

To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we start by breaking it down.

1. **Factor out the numerator**:
\[
4x^2 - 12x + 24
\]
We can factor out 4 from each term:
\[
= 4(x^2 - 3x + 6)
\]

2. **Rewrite the expression**:
Now substitute this back into the original expression:
\[
\frac{4(x^2 - 3x + 6)}{4x}
\]

3. **Cancel common factors**:
The \(4\) in the numerator and the \(4\) in the denominator can be canceled:
\[
= \frac{x^2 - 3x + 6}{x}
\]

4. **Divide each term in the numerator by \(x\)**:
This gives us:
\[
= \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x}
\]
Simplifying the terms:
\[
= x - 3 + \frac{6}{x}
\]

5. **Write the answer in standard form**:
The standard form is typically expressed with the polynomial part first followed by the rational part:
\[
= x - 3 + \frac{6}{x}
\]

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