Question

Answer 1

a:

ĐKXĐ: x>0; x<>1

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

\(=\frac{1+\sqrt{x}-1+\sqrt{x}}{\left(1-\sqrt{x}\right)\left(1+\sqrt{x}\right)}\cdot\frac{1-\sqrt{x}}{\sqrt{x}}=\frac{2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}=\frac{2}{\sqrt{x}+1}\)

b: Khi x=1/9 thì \(A=\frac{2}{\sqrt{\frac19}+1}=2:\left(\frac13+1\right)=2:\frac43=2\cdot\frac34=\frac32\)

c: A nguyên

=>2⋮\(\sqrt{x}+1\)

=>\(\sqrt{x}+1\in\left\lbrace1;2\right\rbrace\)

=>\(\sqrt{x}\in\left\lbrace0;1\right\rbrace\)

=>x∈{0;1}

Kết hợp ĐKXĐ, ta được: x∈∅