Question

Докажите, что: 1/(√5 +1) +1/(√5+3)+1/√5=1/2+√5/5

Answer 1

(√5-1)/[(√5+1)(√5-1)]+(√5-3)/[(√5+3)(√5-3)+√5/5=
=(√5-1)/(5-1)+(√5-3)/(5-9)+√5/5=(√5-1)/4-(√5-3)/4+√5/5=
=(√5-1-√5+3)/4+√5/5=2/4+√5/5=1/2+√5/5