[tex][(3+4)^{-1}+\frac{1}{\sqrt7}]\div(1+\sqrt7)=(7^{-1}+\frac{\sqrt7}{7})\cdot\frac{1}{1+\sqrt7}\\=(\frac{1}{7}+\frac{\sqrt7}{7})\cdot\frac{1}{1+\sqrt7}=\frac{1+\sqrt7}{7}\cdot\frac{1}{1+\sqrt7}\\
\text{Se simplific\u a } 1+\sqrt7 \text{ de la numitor cu cel de la num\u ar\u ator:}\\
\frac{1+\sqrt7}{7}\cdot\frac{1}{1+\sqrt7}=\frac{1}{7}[/tex]
