Question: Which of the following rational expressions has domain restrictions $x \neq 4$ and $x \neq -3$?
1. $\frac{5(x - 4)}{x + 3}$
2. $\frac{(x + 2)(x + 3)}{(x + 3)(x - 4)}$
3. $\frac{13(x - 1)(x + 2)}{x(x - 3)(x + 4)}$
4. $\frac{(x + 3)(x - 4)}{(x + 2)(x - 1)}$
1. **State the problem:** We need to find which rational expression has domain restrictions $x \neq 4$ and $x \neq -3$.
2. **Recall domain restrictions:** The domain restrictions for a rational expression come from values of $x$ that make the denominator zero.
3. **Analyze each expression's denominator:**
- Expression 1 denominator: $x + 3 = 0 \Rightarrow x = -3$
- Expression 2 denominator: $(x + 3)(x - 4) = 0 \Rightarrow x = -3$ or $x = 4$
- Expression 3 denominator: $x(x - 3)(x + 4) = 0 \Rightarrow x = 0$, $x = 3$, or $x = -4$
- Expression 4 denominator: $(x + 2)(x - 1) = 0 \Rightarrow x = -2$ or $x = 1$
4. **Compare domain restrictions:**
- Expression 1 restricts $x \neq -3$ only.
- Expression 2 restricts $x \neq -3$ and $x \neq 4$.
- Expression 3 restricts $x \neq 0$, $x \neq 3$, and $x \neq -4$.
- Expression 4 restricts $x \neq -2$ and $x \neq 1$.
5. **Conclusion:** Expression 2 has the domain restrictions $x \neq 4$ and $x \neq -3$.
**Final answer:** Expression 2