a/ Rút gọn D
D = \(\left(\frac{\sqrt{x}}{2}-\frac{1}{2\sqrt{x}}\right)\)\(\left(\frac{\chi+\sqrt{x}}{\sqrt{x}+1}-\frac{x+\sqrt{x}}{\sqrt{x}-1}\right)\)
= \(\left(\frac{x}{2\sqrt{x}}-\frac{1}{2\sqrt{x}}\right)\)\(\left[\frac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(x+\sqrt{x}\right)}{\left(\sqrt[]{x}-1\right)\left(\sqrt{x}+1\right)}\right]\)
= \(\frac{x-1}{2\sqrt{x}}\)\(\left[\frac{x\sqrt{x}+x-x-\sqrt{x}-\left(x\sqrt{x}+x+x+\sqrt{x}\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right]\)
= \(\frac{x-1}{2\sqrt{x}}\)\(\left[\frac{x\sqrt{x}+x-x-\sqrt{x}-x\sqrt{x}-x-x-\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right]\)
=\(\frac{x-1}{2\sqrt{x}}\) \(\frac{-2x-2\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
=\(\frac{x-1}{2\sqrt{x}}\) \(\frac{-2\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
= \(-\sqrt{x}-1\)
b/Tìm x để D > -6
Ta có D> -6
hay \(-\sqrt{x}-1\)> -6
⇔ \(-\sqrt{x}\)> -5
⇔ \(\sqrt{x}\) < 5
⇔ \(x\) <25
Chúc bạn học tốt ;>
