Question

Answer 1

a)ĐKXĐ:x≠0;x≠1

b)\(C=\left(x-3+\dfrac{1}{x-1}\right):\left(x-1-\dfrac{1}{x-1}\right):\dfrac{x+2}{x}\)

\(=\dfrac{\left(x-3\right)\left(x-1\right)+1}{x-1}:\dfrac{\left(x-1\right)^2-1}{x-1}:\dfrac{x+2}{x}\)

\(=\dfrac{x^2-4x+4}{x^2-2x}.\dfrac{x}{x+2}=\dfrac{\left(x-2\right)^2.x}{x\left(x-2\right)\left(x+2\right)}=\dfrac{x-2}{x+2}\)

c)\(x=\sqrt{6+\sqrt{20}}=\sqrt{5+2\sqrt{5}.\sqrt{1}+1}=\sqrt{5}+1\)

\(\Rightarrow c=\dfrac{\sqrt{5}+1-2}{\sqrt{5}+1+2}=\dfrac{\sqrt{5}-1}{\sqrt{5}+3}=-2+\sqrt{5}\)