Evaluate the limit of $(\sqrt{5-x}-2)/(\sqrt{2-x}-1)$ as $x\to 1$

Question

Can you help me with it and explain the steps

$$\lim_{x \to 1} \frac{\sqrt{5-x}-2}{\sqrt{2-x}-1}$$

I tried to multiply at conjugate expression but I failed.

Answer 1

Hint: $$\frac{\sqrt{5-x}-2}{\sqrt{2-x}-1}=\frac{(\sqrt{5-x}-2)(\sqrt{5-x}+2)(\sqrt{2-x}+1)}{(\sqrt{2-x}-1)(\sqrt{2-x}+1)(\sqrt{5-x}+2)}.$$

Answer 2

You could multiply by $(\sqrt{5-x}+2)(\sqrt{2-x}+1)$ both the numerator and denominator of this fraction.