Question

Rút gọn biểu thức\(\dfrac{2+\sqrt x}{2-\sqrt x} - \dfrac{2-\sqrt x}{2+\sqrt x} -\dfrac{4}{x-4} \)

Answer 1

ĐKXĐ: x ≥ 0; x ≠ 4

Khi đó ta có:

\(\dfrac{2+\sqrt{x}}{2-\sqrt{ }x}\) \(-\dfrac{2-\sqrt{x}}{2+\sqrt{x}}\)\(-\dfrac{4}{x-4}\)

= \(\dfrac{\left(2+\sqrt{x}\right)\left(2+\sqrt{x}\right)}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\)\(-\dfrac{\left(2-\sqrt{x}\right)\left(2-\sqrt{x}\right)}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}\)\(+\dfrac{4}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}\)

= \(\dfrac{\left(4+4\sqrt{x}+x\right)-\left(4-4\sqrt{x}+x\right)+4}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}\)

= \(\dfrac{8\sqrt{x}+4}{x-4}\)