Question

(x^2 - 3x) / (3x - 3)

In the equation listed above, can I cancel out the 3x from both the numerator and denominator?

Answer 1

No, you cannot directly cancel out \( 3x \) from both the numerator and the denominator in the expression \( \frac{x^2 - 3x}{3x - 3} \). This is because you can only cancel out a factor that is common to both the numerator and the denominator.

First, let's factor both the numerator and the denominator:

1. **Numerator**: \( x^2 - 3x = x(x - 3) \)
2. **Denominator**: \( 3x - 3 = 3(x - 1) \)

So, our expression can be rewritten as:

\[
\frac{x(x - 3)}{3(x - 1)}
\]

Now you can see that there are no common factors between the numerator and the denominator that allow for cancellation. Therefore, you cannot cancel \( 3x \). The simplification is:

\[
\frac{x(x - 3)}{3(x - 1)}
\]

This is the simplest form of the expression.