# Math Help - Easy- Limit

1. ## Easy- Limit

$\lim_{x\to\0}\frac{x}{\frac{1}{6}+\frac{1}{x-6}}$ I keep getting 36(36), actual answer is-36.

I get $\frac{x(6(x-6))}{\frac{6+x-6}{6(x-6)}}$ which equals $(6(x-6))(6(x-6))$

What have I done wrong?

2. ## Re: Easy- Limit

Originally Posted by Greymalkin
$\lim_{x\to\0}\frac{x}{\frac{1}{6}+\frac{1}{x-6}}$ I keep getting 36(36), actual answer is-36.
I get $\frac{x(6(x-6))}{\frac{6+x-6}{6(x-6)}}$ which equals $(6(x-6))(6(x-6))$
$\frac{x}{\frac{1}{6}+\frac{1}{x-6}}=\frac{6x(x-6)}{x}=6x-36$