Computing the standard part of $(3-\sqrt{c+2})/(c-7)$ where the standard part of $c$ is $7$

Question

I'm working through Keisler's calculus book based on infinitesimals. The following problem has me a little bit stumped.

Compute the standard part of: $$\frac{3-\sqrt{c+2}}{c-7}$$ Given that $c\ne7$ and $st(c) = 7$ where $st(x)$ is the standard part function. I know that $$\lim_{c\to7}{\frac{3-\sqrt{c+2}}{c-7}}=-\frac{1}{6}$$ I can't for the life of me though figure out how to work this out using standard parts. I'm probably being dumb. Help?

Answer 1

HINT: Try multiplying by $\frac{3+\sqrt{c+2}}{3+\sqrt{c+2}}$