Question

rút gọn : (x+3/x-9 +1/căn x +3 ):căn x /căn x trừ 3

Answer 1

\(\left(\dfrac{x+3}{x-9}+\dfrac{1}{\sqrt{x}+3}\right):\dfrac{\sqrt{x}}{\sqrt{x}-3}\)

\(=\left(\dfrac{\left(x+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}+\dfrac{1}{\sqrt{x}+3}\right).\dfrac{\sqrt{x}-3}{\sqrt{x}}\)

\(=\left(\dfrac{x+3+\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right).\dfrac{\sqrt{x}-3}{\sqrt{x}}\)

\(=\left(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right).\dfrac{\sqrt{x}-3}{\sqrt{x}}\)

\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\)