Limits by rationalizing

Example §

g(x) = $\frac{x+1}{\sqrt{x+5}-2}$

To rationalize this you would multiply the numerator and denominator by

$\sqrt{x+5}$ + 2

Resulting in: $\frac{x+1}{\sqrt{x+5}-2}$ $\cdot$ $\frac{\sqrt{x+5}+2}{\sqrt{x+5}+2}$ = $\sqrt{x+5}$ + 2

lim $\sqrt{x+5}$ + 2 = 4 x -> -1

Solved Examples §