Question

Answer 1

a: Thay x=9 vào A, ta được:

\(A=\frac{\sqrt9-2}{\sqrt9+1}=\frac{3-2}{3+1}=\frac14\)

b: \(B=\frac{5}{\sqrt{x}+2}+\frac{1}{2-\sqrt{x}}+\frac{x+16}{x-4}\)

\(=\frac{5}{\sqrt{x}+2}-\frac{1}{\sqrt{x}-2}+\frac{x+16}{x-4}\)

\(=\frac{5\left(\sqrt{x}-2\right)-\sqrt{x}-2+x+16}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{5\sqrt{x}-10+x-\sqrt{x}+14}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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