Question

Simplify 4x²-12x+24 / 4x
Write your answer in standard form.

Answer 1

To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we can first factor the numerator.

The numerator \(4x^2 - 12x + 24\) can be factored out by noticing that each term is divisible by 4:

\[
4(x^2 - 3x + 6)
\]

So we rewrite the expression as:

\[
\frac{4(x^2 - 3x + 6)}{4x}
\]

Now, we can cancel the 4 in the numerator and the denominator:

\[
\frac{x^2 - 3x + 6}{x}
\]

Next, we can separate the fraction:

\[
\frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x}
\]

This simplifies to:

\[
x - 3 + \frac{6}{x}
\]

Thus, the simplified form of the expression in standard form is:

\[
x - 3 + \frac{6}{x}
\]

If desired, we can also write it as:

\[
x - 3 + 6x^{-1}
\]

However, the most straightforward standard form is:

\[
x - 3 + \frac{6}{x}
\]