## Zadatak B-1.2.

Izračunajte

$$
\frac{1-\frac{1}{x^{2}}}{1+\frac{6}{x}+\frac{5}{x^{2}}} \cdot \frac{x+5}{x-1}
$$


Rješenje.

$$
\begin{aligned}
\frac{1-\frac{1}{x^{2}}}{1+\frac{6}{x}+\frac{5}{x^{2}}} \cdot \frac{x+5}{x-1} & =\frac{\frac{x^{2}-1}{x^{2}}}{\frac{x^{2}+6 x+5}{x^{2}}} \cdot \frac{x+5}{x-1}= \\
& =\frac{(x-1) \cdot(x+1)}{(x+1) \cdot(x+5)} \cdot \frac{x+5}{x-1}=1
\end{aligned}
$$

$x \neq 1,0,-1,-5$

