Question

Выражение и найдите его значение при x=1,5 x+1. x-1. x^2+1. x^2-1 ( - ) : ( - ) x-1. x+1. x^2-1. x^+1

Answer 1

$(\frac{x+1}{x-1}+\frac{x-1}{x+1}):(\frac{x^{2}+1}{x^{2}-1}-\frac{x^{2}-1}{x^{2}+1})=$

$\frac{(x+1)^{2}-(x-1)^{2}}{x^{2}-1}:\frac{(x^{2}+1)^{2}-(x^{2}-1)^{2}}{(x^{2}-1)(x^{2}+1)}=$

$\frac{(x+1+x-1)(x+1-x+1)(x^{2}-1)(x^{2}+1)}{(x^{2}-1)(x^{2}+1+x^{2}-1)(x^2+1-x^2+1)}=$

$\frac{2x*2(x^{2}+1)}{2x^{2}*2}=\frac{x^{2}+1}{x}$

$\frac{1,5^{2}+1}{1,5}=\frac{2,25+1}{1,5}=\frac{3,25}{1,5}=\frac{65}{30}=\frac{13}{6}=2\frac{1}{6}$