Đáp án:
Giải thích các bước giải:
a)A=\(\frac{x}{x-4}+\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\)
=\(\frac{x+\sqrt{x}-2+\sqrt{x}+2}{(\sqrt{x}-2)(\sqrt{x}+2)}\)
=\(\frac{x+\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)}\)
=\(\frac{\sqrt{x}(\sqrt{x}+2)}{(\sqrt{x}-2)(\sqrt{x}+2)}\)
=\(\frac{\sqrt{x}}{\sqrt{x}-2}\)
b) A=\(\frac{\sqrt{x}}{\sqrt{x}-2}=\frac{\sqrt{25}}{\sqrt{25}-2}=\frac{5}{3}\)
c) A=\(\frac{\sqrt{x}}{\sqrt{x}-2}=\frac{\sqrt{x}-2+2}{\sqrt{x}-2}=1+\frac{2}{\sqrt{x}-2}\)
\(\frac{2}{\sqrt{x}-2}∈Z⇒ 2\vdots \sqrt{x}-2\)⇒ ƯC={±1,±2}
·\(\sqrt{x}-2=1⇒\sqrt{x}=3⇒ x=9\)
·\(\sqrt{x}-2=-1⇒\sqrt{x}=1⇒ x=1\)
·\(\sqrt{x}-2=2⇒\sqrt{x}=4⇒ x=16\)
·\(\sqrt{x}-2=-2⇒\sqrt{x}=0⇒ x=0( nhận)\)
Vậy S={0}
