Question

(x -2*căn bậc hai(x) + 8)/(x-4) - 2/(căn bậc hai(x) -2)

Answer 1

Ta có: \(\frac{x-2\sqrt{x}+8}{x-4}-\frac{2}{\sqrt{x}-2}\)

\(=\frac{x-2\sqrt{x}+8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{2\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(=\frac{x-2\sqrt{x}+8-2\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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

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

\(=\frac{\sqrt{x}-2}{\sqrt{x}+2}\)