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**rowe** $\displaystyle \lim_{x \to -3} \frac{t^2-9}{2t^2 +7t+3}$ will equal 0 if you apply the usual limit laws and consider the limit as t tends to -3 in the numerator.

Factorisation of the numerator and denominator gives us $\displaystyle \frac{t-3}{2t+1}$, which gives us the correct limit $\displaystyle \frac{6}{5}$. However, I only know this because I looked at the graph.

It seems arbitrary that a simplification should produce a different result, if the expression is equal. How can I possibly tell whether a function has a limit at a particular point unless I do the "correct" manipulations? There must be some strict method I can apply to every function to ensure I know I am taking limits correctly.