Math Help - Help evaluating the limits of these two problems, one of which is a complex fraction

1. Help evaluating the limits of these two problems, one of which is a complex fraction

I like finding limits, but complex fractions and I do not get along. I would greatly appreciate it if someone could help me evaluate the limits of the following two problems (step-by-step). For #37, I received a different answer from Mathway.com, which was also a different answer from the back of my book, so I am very lost. I appreciate the help!

Thank you!

2. Re: Help evaluating the limits of these two problems, one of which is a complex fract

Actually, I figured out #38 (the formatting threw me off, but it was easy), so I just need help with number #37. Thank you!! :-)

3. Re: Help evaluating the limits of these two problems, one of which is a complex fract

Hello, dannibambi!

$37.\;\lim_{x\to\text{-}4} \dfrac{\frac{1}{4} + \frac{1}{x}}{x+4}$

Multiply by $\frac{4x}{4x}\!: \;\;\dfrac{4x\left(\frac{1}{4} + \frac{1}{x}\right)}{4x(x+4)} \;=\; \frac{x+4}{4x(x+4)} \;=\;\frac{1}{4x}$

Therefore: . $\lim_{x\to\text{-}4}\frac{1}{4x} \;=\;-\frac{1}{16}$

5. Re: Help evaluating the limits of these two problems, one of which is a complex fract

Originally Posted by ibdutt
I expect you meant to write "lim" instead of "log"...

6. Re: Help evaluating the limits of these two problems, one of which is a complex fract

Thank you so much!! I can't believe I over-thought it that much. I was trying to multiply the numerator by 4+x and not multiply the denominator by anything...hence my headache-on-top-of-headache... Thanks!! :-)