Упростите: [tex](\frac{1}{\sqrt{a}+\sqrt{a+1} }+\frac{1}{\sqrt{a}-\sqrt{a-1} } ):(1+\sqrt{\frac{a+1}{a-1} } )[/tex]. Created by Edward2121. algebra-ru

tex]...

Edward2121 @Edward2121

August 2022 1 28 Report

Упростите:
[tex](\frac{1}{\sqrt{a}+\sqrt{a+1} }+\frac{1}{\sqrt{a}-\sqrt{a-1} } ):(1+\sqrt{\frac{a+1}{a-1} } )[/tex]

Answers & Comments

Universalka

Verified answer

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

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

2 votes Thanks 2

Edward2121 ОГРОМНОЕ СПАСИБО ВАМ !!!

Universalka Всегда рада помочь )

Answers & Comments

Verified answer

4x 153 2 x0 pomogite

2...

x 1 82x 1 najdite umnozhenie kornej

reshite sistemnoe uravnenie yx7x11 yy3x15

pomogite reshit sistemnoe uravnenie844b43c91d1cfd86a2b9516f01a85d0e 69225

tex]...

tex]...

nazovite avscissu tochki peresechenie pryamyh uah5 i 2u 3hv0 znaya chto pervaya pr

iz posyolka v gorod idyot avtobus i kazhdye 15 minut on vstrechaet avtobus kotoryjca136a08ddca3c83b1982c8d515bae75 95682

dvuznachnoe chislo ravno summe chisla disyatkov i kvadrata chisla edinicnazovite sum

рекомендуемые вопросы

Helpful Links

Helpful Social