Ответы и объяснения

  • Yena
  • главный мозг
2013-03-14T22:58:50+00:00

\frac{log_2(1+\frac{1}{x-1})}{log_2(x-1)*log_2x}+\frac{log_2(1+\frac{1}{x})}{log_2(x+1)*log_2x}=

=\frac{log_2\frac{x-1+1}{x-1}}{log_2(x-1)*log_2x}+\frac{log_2\frac{x+1}{x}}{log_2(x+1)*log_2x}=\frac{log_2\frac{x}{x-1}}{log_2(x-1)*log_2x}+\frac{log_2\frac{x+1}{x}}{log_2(x+1)*log_2x}

=\frac{log_2x-log_2(x-1)}{log_2(x-1)*log_2x}+\frac{log_2(x+1)-log_2x}{log_2(x+1)*log_2x}=

\frac{log_2(x+1)*log_2x-log_2(x+1)*log_2(x-1)+log_2(x-1)*log_2(x+1)-log_2(x-1)*log_2x}{log_2(x+1)*log_2(x-1)*log_2x}=

=\frac{log_2x(log_2(x+1)-log_2(x-1))}{log_2(x+1)*log_2(x-1)*log_2x}=\frac{log_2(x+1)-log_2(x-1)}{log_2(x+1)*log_2(x-1)}=

\frac{log_2\frac{x+1}{x-1}}{log_2(x+1)*log_2(x-1)}

 

 

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