Question

a. rút gọn biểu thức B

b.tìm x để biểu thức M=A.b nhận giá trị nguyên

B=\(B=\dfrac{\sqrt{X}+1}{\sqrt{X}-2}+\dfrac{\sqrt{X}+2}{1-\sqrt{X}}+\dfrac{\sqrt{X}-4}{\left(\sqrt{X}-1\right)\left(\sqrt{X}-2\right)}\)

Answer 1

a: \(B=\frac{\sqrt{x}+1}{\sqrt{x}-2}+\frac{\sqrt{x}+2}{1-\sqrt{x}}+\frac{\sqrt{x}-4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}-1}+\frac{\sqrt{x}-4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)+\sqrt{x}-4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{x-1-x+4+\sqrt{x}-4}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}=\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}=\frac{1}{\sqrt{x}-2}\)