Mathematics

Problem

A rational function is defined by

L(x)=\frac{\sqrt{x+7}-3}{x^{2}-4}.

Throughout this problem,

x

is assumed to be close to

2

but not equal to

2

. a. Rewrite

L(x)

into an algebraically equivalent form that does not contain a radical expression in the numerator and clearly exhibits all factors that may cancel. Show every intermediate algebraic step. b. Using the expression obtained in part (a), determine

\displaystyle \lim_{x\to 2}L(x)

. Give a brief justification for each step leading to the numerical value.

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