How to solve $\displaystyle\lim_{x\to 0}\tfrac{\sqrt{x+25}-5} {\sqrt{x+16}-4}$ \begin{eqnarray}
\\&\lim_{x\to 0}\frac{\sqrt{x+25}-5} {\sqrt{x+16}-4}
\end{eqnarray}
Undefined limit
\begin{eqnarray}
\frac{0} {0}
\end{eqnarray}

Given $\displaystyle \lim_{x\to 0}\frac{\sqrt{x+25}-5}{\sqrt{x+16}-4} \times \frac{\sqrt{x+16}+4}{\sqrt{x+16}+4} \times \frac{\sqrt{x+25}+5}{\sqrt{x+25}+5}$
We Get $\displaystyle \lim_{x\rightarrow 0} \frac{x}{x} \times \frac{\sqrt{x+16}+4}{\sqrt{x+25}+5} = \frac{8}{10}$
