Question

SIMPLIFICAR B= = √(n-1&(5^(n+1)+1)/(5^(1-n)+1))-√(n&(10^n+15^n+6^n)/(5^(-n)+2^(-n)+3^(-n) ))

Answer 1

Al Simplificar B una función racional y exponencial:

B = $\sqrt{\frac{5^{1-n}n+n-5^{n+1}+1}{5^{1-n}+1}}) - \sqrt{(\frac{(10^{n}+15^{n}+6^{n} )n}{(5^{-n}+2^{-n}+3^{-n} )} )}$

Dada:

B = $\sqrt{(n-1.\frac{(5^{n+1}+1 )}{(5^{1-n}+1 )}}) - \sqrt{(n.\frac{(10^{n}+15^{n}+6^{n} )}{(5^{-n}+2^{-n}+3^{-n} )} )}$

$\sqrt{(n-1.\frac{(5^{n+1}+1 )}{(5^{1-n}+1 )}})$

Iniciamos por el numerador;

$1.(5^{n+1}+1 )$

Multiplicamos por 1 y quitamos el paréntesis;

= $5^{n+1}+1$

Simplificamos  $n-\frac{(5^{n+1}+1 )}{(5^{1-n}+1 )}$ en la fracción;

=  $\frac{n(5^{1-n}+1 )-(5^{n+1}+1 )}{(5^{1-n}+1 )}}$

Expandir;

$n(5^{1-n}+1 )-(5^{n+1}+1 )$

= $n5^{1-n}+n-5^{n+1}+1$

=$\sqrt{\frac{5^{1-n}n+n-5^{n+1}+1}{5^{1-n}+1}})$

La segunda parte;

$\sqrt{(n.\frac{(10^{n}+15^{n}+6^{n} )}{(5^{-n}+2^{-n}+3^{-n} )} )}$

se multiplica n al numerador;

$n.(10^{n}+15^{n}+6^{n})$

= $\frac{(10^{n}+15^{n}+6^{n})n }{5^{-n}+2^{-n}+3^{-n} }$

= $\sqrt{(\frac{(10^{n}+15^{n}+6^{n} )n}{(5^{-n}+2^{-n}+3^{-n} )} )}$

= $\sqrt{\frac{5^{1-n}n+n-5^{n+1}+1}{5^{1-n}+1}}) - \sqrt{(\frac{(10^{n}+15^{n}+6^{n} )n}{(5^{-n}+2^{-n}+3^{-n} )} )}$