Question

Answer 1

a: ĐKXĐ: x>=0; x<>1

b: \(P=\frac{\sqrt{x}}{\sqrt{x}+1}+\frac{2}{\sqrt{x}-1}-\frac{x-2\sqrt{x}+5}{x-1}\)

\(=\frac{\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}+1\right)-x+2\sqrt{x}-5}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)

\(=\frac{x-\sqrt{x}+2\sqrt{x}+2-x+2\sqrt{x}-5}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{3\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{3}{\sqrt{x}+1}\)

c: Để P là số nguyên thì 3⋮\(\sqrt{x}+1\)

=>\(\sqrt{x}+1\in\left\lbrace1;3\right\rbrace\)

=>\(\sqrt{x}\in\left\lbrace0;2\right\rbrace\)

=>x∈{0;4}