Question

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

Answer 1

$left ( frac{1}{sqrt{p}+sqrt{p+1}}+frac{1}{sqrt{p}-sqrt{p+1}}right ): left (1+sqrt{frac{p+1}{p-1}} right )=\\=frac{sqrt{p}-sqrt{p+1}+sqrt{p}+sqrt{p+1}}{(sqrt{p}+sqrt{p+1})(sqrt{p}-sqrt{p+1})}:frac{sqrt{p-1}+sqrt{p+1}}{sqrt{p-1}}=\\= frac{2sqrt{p}}{p-(p+1)}cdot frac{sqrt{p-1}}{sqrt{p-1}+sqrt{p+1}} = frac{2p}{-1}cdot frac{sqrt{p-1}}{sqrt{p-1}+sqrt{p+1}} =- frac{2psqrt{p-1}}{sqrt{p-1}+sqrt{p+1}}$