Evaluate $\lim_{x\to0} \frac{6}{x}-\frac{42}{x^2+7x}$ Evaluate $\lim_{x\to0} \frac{6}{x}-\frac{42}{x^2+7x}$
I'm I want to say that you cross multiply to get the same denominator, but I could be wrong.
Please Help!!

You are correct that a common denominator is necessary:
\begin{align}
\frac 6 x - \frac {42} {x^2 + 7x} &= \frac 6 x - \frac {42} {x(x + 7)}\\
&= \frac{6(x + 7) - 42}{x(x + 7)} \\
&= \frac{6x}{x(x + 7)} \\
&= \frac{6}{x + 7}
\end{align}
for $x \ne 0$. Do you see how to compute the limit now?
