Question

Cho A = 1 : \(\left(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\right)\).

a) Rút gọn

b) So sánh A với 3

Answer 1

a/ ĐKXĐ: \(x\ge0;x\ne1\)

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

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

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

b/ Cho x bằng bao nhiêu đi rồi ms so sánh đc, ko thì phải chia trường hợp :)