Question

Rút gọn biểu thức N = \(\frac{x+12}{x-4}\)+ \(\frac{1}{\sqrt{x}+2}\) - \(\frac{4}{\sqrt{x}-2}\)

HELP MEEEE

Answer 1

ĐKXĐ: \(x\ge0;x\ne4\)

\(N=\frac{x+12}{x-4}+\frac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{4\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

\(N=\frac{x+12}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{4\sqrt{x}+8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}=\frac{x-3\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)

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