How do I solve this limit without the L'hopital's rule?

Question

$$\lim\limits_{x\to 2} \frac{ 2x^2-5x+2 }{ \sqrt{2+x}-\sqrt{2x} }$$

Thanks

Answer 1

note that $$2x^2-5x+2=(2x-1)(x-2)$$ and we have by multiplication of numerator and denominator with $\sqrt{2+x}+\sqrt{2x}$ the following term $$\frac{(2x-1)(x-2)(\sqrt{2+x}+\sqrt{2x})}{-(x-2)}$$