Question

simplify 2/√5-√3-1/√5-2

Answer 1

Answer:

$\frac{2}{ \sqrt{5} } - \frac{ \sqrt{3} - 1}{ \sqrt{5} - 2 } \\ = \frac{2}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } = \frac{2 \sqrt{5} }{5} \\ \frac{ \sqrt{3} - 1}{ \sqrt{3} - 2 } \times \frac{ \sqrt{3} + 2}{ \sqrt{3} + 2} = \frac{3 + 2 \sqrt{3} - \sqrt{3} - 2 }{3 - 2} \\ = \frac{ \sqrt{3} }{1} = \sqrt{3} \\ \frac{2 }{ \sqrt{5} } - \frac{ \sqrt{3} - 1 }{ \sqrt{5 } - 2} = \frac{2 \sqrt{5} }{5} - \sqrt{3} \\ = \frac{2 \sqrt{5} - 5 \sqrt{3} }{5}$