Question

Упростите:
$(frac{1}{sqrt{a}+sqrt{a+1} }+frac{1}{sqrt{a}-sqrt{a-1} } ):(1+sqrt{frac{a+1}{a-1} } )$

Answer 1

$1)frac{1}{sqrt{a}+sqrt{a+1}}+frac{1}{sqrt{a}-sqrt{a-1}}=frac{sqrt{a}-sqrt{a+1}}{(sqrt{a}+sqrt{a+1})(sqrt{a}-sqrt{a+1})}+frac{sqrt{a}+sqrt{a-1}}{(sqrt{a}-sqrt{a-1})(sqrt{a}+sqrt{a-1}}=frac{sqrt{a}-sqrt{a+1}}{a-a-1}+frac{sqrt{a}+sqrt{a-1}}{a-a+1}=sqrt{a}+sqrt{a-1}-sqrt{a}+sqrt{a+1}=sqrt{a-1}+sqrt{a+1}$

$2)1+sqrt{frac{a+1}{a-1} }=1+frac{sqrt{a+1} }{sqrt{a-1} }=frac{sqrt{a-1}+sqrt{a+1}}{sqrt{a-1} }\\3)(sqrt{a-1}+sqrt{a+1}):frac{sqrt{a-1}+sqrt{a+1}}{sqrt{a-1} }=(sqrt{a-1}+sqrt{a+1})*frac{sqrt{a-1} }{sqrt{a-1}+sqrt{a+1}}=sqrt{a-1}$

Answer 2

ОГРОМНОЕ СПАСИБО ВАМ !!!

Answer 3

Всегда рада помочь )