Question

Rút gọn B = \(\left(\frac{x+\sqrt{y}+\sqrt{xy}-1}{\sqrt{x}+1}+1\right).\left(\sqrt{x}-\sqrt{y}\right)\)

Answer 1

ĐKXĐ: \(x\ge0;y\ge0\)

Ta có B = \(\left(\frac{\left(x-1\right)+\left(\sqrt{y}+\sqrt{xy}\right)}{\sqrt{x}+1}+1\right)\left(\sqrt{x}-\sqrt{y}\right)\)

= \(\left(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)+\sqrt{y}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}\right)\)\(\left(\sqrt{x}-\sqrt{y}\right)\)

= \(\left(\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1+\sqrt{y}\right)}{\sqrt{x}+1}+1\right)\left(\sqrt{x}-\sqrt{y}\right)\)

= \(\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)\)

= \(x-y\)

Vậy B = x - y