Question

\(\dfrac{7+5\sqrt{3}}{3\sqrt{3}+5}\)

*trình bày cụ thể ạ,Tks

Answer 1

\(\dfrac{7+5\sqrt{3}}{3\sqrt{3}+5}\\ =\dfrac{\left(7+5\sqrt{3}\right)\left(3\sqrt{3}-5\right)}{\left(3\sqrt{3}+5\right)\left(3\sqrt{3}-5\right)}\\ =\dfrac{21\sqrt{3}-35+45-25\sqrt{3}}{\left(3\sqrt{3}\right)^2-5^2}\\ =\dfrac{-4\sqrt{3}+10}{27-25}\\ =\dfrac{2\left(-2\sqrt{3}+5\right)}{2}\\ =5-2\sqrt{3}\)

Answer 2

\(\dfrac{7+5\sqrt{3}}{3\sqrt{3}+5}\)

\(=\dfrac{\left(7+5\sqrt{3}\right)\left(3\sqrt{3}-5\right)}{\left(3\sqrt{3}+5\right)\left(3\sqrt{3}-5\right)}\)

\(=\dfrac{21\sqrt{3}-35+45-25\sqrt{3}}{27-25}\)

\(=\dfrac{10-4\sqrt{3}}{2}\)

\(=5-2\sqrt{3}\)