Question: (x + 5) / (\sqrt{x} + 7 - 2)
1. **State the problem:** Simplify the expression $$\frac{x + 5}{\sqrt{x} + 7 - 2}$$.
2. **Simplify the denominator:** Combine like terms in the denominator:
$$\sqrt{x} + 7 - 2 = \sqrt{x} + 5$$
3. **Rewrite the expression:**
$$\frac{x + 5}{\sqrt{x} + 5}$$
4. **Check for possible simplification:** Notice that the numerator is $x + 5$ and the denominator is $\sqrt{x} + 5$.
5. **Factor the numerator if possible:**
Since $x = (\sqrt{x})^2$, we can write:
$$x + 5 = (\sqrt{x})^2 + 5$$
This does not factor nicely as a product involving $\sqrt{x} + 5$.
6. **Conclusion:** The expression cannot be simplified further algebraically, so the simplified form is:
$$\frac{x + 5}{\sqrt{x} + 5}$$