Questions: Cancel the common factor of the numerator and the denominator to write the expression in simplified form.

Transcript text: Hide Sample Answer \[ \begin{aligned} \frac{4 x^{2}-14 x+6}{x^{3}-7 x^{2}+12 x} & =\frac{2\left(2 x^{2}-7 x+3\right)}{x\left(x^{2}-7 x+12\right)} \\ & =\frac{2[(x-3)(2 x-1)]}{x[(x-4)(x-3)]} \end{aligned} \] Part C Cancel the common factor of the numerator and the denominator to write the expression in simplified form.

Solution

Solution Steps

Step 1: Identify the Common Factor

The given expression is:

\[ \frac{2[(x-3)(2x-1)]}{x[(x-4)(x-3)]} \]

We need to identify the common factor in the numerator and the denominator. Observing the expression, we see that \((x-3)\) is a common factor in both the numerator and the denominator.

Step 2: Cancel the Common Factor

Cancel the common factor \((x-3)\) from both the numerator and the denominator:

\[ \frac{2[(x-3)(2x-1)]}{x[(x-4)(x-3)]} = \frac{2(2x-1)}{x(x-4)} \]