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How to solve limits with basic algebra?

How to Solve Limits with Basic Algebra. When substitution doesn't work in the original limit function - usually because of a hole in the function - you can often use some algebra to manipulate the function until substitution does work (it works because your manipulation plugs up the hole). You can try various things from Algebra I, like adding or subtracting fractions, multiplying or dividing fractions, canceling, or some other form of simplification.

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