Question

Prove that 1/(2 + √3) + 2/(√5 - √3) + 1/(2 - √5) = 0

Answer 1

Answer: (1/2+√3)+(2/√5-√3)+(1/2-√5)

=1(2-√3)/(2-√3)(2+√3)+2(√5+√3)/(√5+√3)(√5-√3)+1(2+√5)/(2+√5)(2-√5)

=(2-√3)/{2²-(√3)²}+2(√5+√3)/{(√5)²-(√3)²}+(2+√5)/{2²-(√5)²}

=(2-√3)/(4-3)+2(√5+√3)/(5-3)+(2+√5)/(4-5)

=2-√3+{2(√5+√3)/2}-(2+√5)

=2-√3+√5+√3-2-√5

=0

[proved]