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**Fenixx09** $\displaystyle \\ \begin{array}{c}\lim\\t\rightarrow0\end{array} \ \ \frac{t+\frac{a}{t}}{t+\frac{b}{t}} \\ \\ \\ \begin{array}{c}\lim\\t\rightarrow0\end{array} \ \ \frac{t^{2}+at}{t^{2}+bt} \\ \\ \\ \begin{array}{c}\lim\\t\rightarrow0\end{array} \ \ \frac{t(t+a)}{t(t+b)}$

The book gives the answer as $\displaystyle \frac{a}{b}$ but I can't figure out how to get to that solution. Up there is everything I have thought of and I'm stuck because it still has a zero in the denominator.

Can anyone give me a hint on what to do (no need to type any LaTeX code)

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Edit: I can't believe I made a mistake simply multiplying $\displaystyle (\frac{a}{t})(t) \& (\frac{b}{t})(t)$