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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!

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Thank you!

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!! :-)

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

Hello, dannibambi!

Quote:

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

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

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

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

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

Quote:

Originally Posted by

**ibdutt**

I expect you meant to write "lim" instead of "log"...

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!! :-)