Finding the limit of function - irrational function How can I find the following limit: 
$$ \lim_{x \rightarrow -1 }\left(\frac{1+\sqrt[5]{x}}{1+\sqrt[7]{x}}\right)$$

Alternate solution: since numerator and denominator each approach 0, we may use L'Hopital's rule.  This gives $\lim_{x\rightarrow -1} \frac{\frac 15 x^{-4/5}}{\frac 17 x^{-6/7}}=\lim_{x\rightarrow -1} \frac{7}{5} x^{6/7-4/5}=\lim_{x\rightarrow -1} \frac{7}{5}x^{2/35}=\frac{7}{5}$
