# Math Help - Limit question.

1. ## Limit question.

I'm going back over my calculus book now that the year is over, doing all the questions to make sure that I know the subject. I worked this limit problem and got it wrong but I don't know how to solve it correctly (without L'Hospital's).
$\lim_{x \to 7} \frac{\sqrt{x+2}-3}{x-7}$

I said DNE, but the answer is 1/6. Anyone know how to solve? thx.

2. Try thinking of the denominator as the "difference of squares" and factoring it.

3. Originally Posted by integral
I'm going back over my calculus book now that the year is over, doing all the questions to make sure that I know the subject. I worked this limit problem and got it wrong but I don't know how to solve it correctly (without L'Hospital's).
$\lim_{x \to 7} \frac{\sqrt{x+2}-3}{x-7}$

I said DNE, but the answer is 1/6. Anyone know how to solve? thx.
Dear integral,

Multiply both the numerator and the denominator by $\sqrt{x+2}+3$.

4. I got it. Thanks