Recently, I learn some basic factorisation techniques, but then there are sometimes where a messy radical will somehow cancel out into a clean one. Here is one I encountered:
$$\frac{3 \sqrt5 - 5}{3 - \sqrt5}$$
Results to $\sqrt5$.
Does anyone have any tips on how I can simplify these radicals, or does it simply require a calculator. Also, can someone fix the formating for me, I'm not sure how to do so.
Thank you!
$$\frac{3\sqrt 5-5}{3-\sqrt 5}\cdot\frac{3+\sqrt 5}{3+\sqrt 5}=\frac{9\sqrt 5+15-15-5\sqrt 5}{9-5}=\frac{4\sqrt 5}{4}=\sqrt 5$$