$$ \begin{array}{ll}1.3 & ext { Given: } \ \begin{array}{ll}\frac{x^{2}-x-6}{3 x-9} \ 1.3 .1 & ext { For which value(s) of } x ext { will the expression be undefined? } \ 1.3 .2 & ext { Simplify the expression fully. }\end{array}\end{array} $$

Question

$$ \begin{array}{ll}1.3 & 	ext { Given: } \ \begin{array}{ll}\frac{x^{2}-x-6}{3 x-9} \ 1.3 .1 & 	ext { For which value(s) of } x 	ext { will the expression be undefined? } \ 1.3 .2 & 	ext { Simplify the expression fully. }\end{array}\end{array} $$

UpStudy AI · Accepted Answer

**Step 1: Determine the values for which the expression is undefined.**

The expression is 
$$
\frac{x^2-x-6}{3x-9}.
$$
It is undefined when the denominator is zero. Set the denominator equal to zero:
$$
3x-9=0.
$$
Solve for $$x$$:
$$
3x = 9 \quad \Longrightarrow \quad x=3.
$$
Thus, the expression is undefined at $$x=3$$.

**Step 2: Simplify the expression.**

First, factor the numerator:
$$
x^2-x-6 = (x-3)(x+2).
$$
The denominator can be factored as:
$$
3x-9 = 3(x-3).
$$
Now, the expression becomes:
$$
\frac{(x-3)(x+2)}{3(x-3)}.
$$
Since $$x \neq 3$$ (as determined in Step 1), we can cancel the common factor $$(x-3)$$:
$$
\frac{x+2}{3}.
$$

**Final Answers:**

1. The expression is undefined when $$x=3$$.

2. The simplified expression is 
$$
\frac{x+2}{3}.
$$
The expression is undefined when $$x=3$$, and it simplifies to $$\frac{x+2}{3}$$.

\( \begin{array}{ll}1.3 & \text { Given: } \\ \begin{array}{ll}\frac{x^{2}-x-6}{3 x-9} \\ 1.3 .1 & \text { For which value(s) of } x \text { will the expression be undefined? } \\ 1.3 .2 & \text { Simplify the expression fully. }\end{array}\end{array} \)

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