Which values of n make the expression -3(n +4)/(n+5) undefined

[GeorgeB]

The question is which values of n make the expression undefined:

-3(n +4)/n+5

No problem with the denominator...it is -5 which will make the denominator = 0. What I am having problems with in the numerator. The book says the correct answer is n=4...my answer was n=-4. I realize the numerator is negative but why should that matter if in the parenthesis (-4+4) = 0 . It then seems to me that it should not matter as -3*0 is still 0. Why does 4 (and not -4) make the numerator/expression undefined?

This is my first post so hope I formatted everything correctly. Thanks.

 

[ksdhart2]

Well, the first thing I'd note is that the expression needs more grouping symbols. From the work you've shown, I'm guessing the original equation was: -3(n+4)/(n+5). That aside, I'm also confused about how your book came to the answer of n=4. There's no value that could make the numerator undefined, but as you've correctly identified, there is one value that results in an undefined expression because of division by zero. Further, you can verify that neither n=4 nor n=-4 result in an undefined expressions by using direct substitution. The only thing I can think of is: are you possibly looking at the answer to a different problem? I've accidentally done that before.

 

[GeorgeB]

Possibly...I have a screen shot of the entire problem so lets see if I can figure out how to post it.

 

[ksdhart2]

The image posted, but unfortunately it's much too small for me to make out what it says.

 

[stapel]

Possibly...I have a screen shot of the entire problem so lets see if I can figure out how to post it.

The screen shot is way too small to read, but it sure looks like the original expression was not what you posted. The numerator looks like it's more like "45 - 3n²", and the denominator looks like it's a quadratic.

Please post the full and exact text of the exercise, from the beginning. Thank you!

 

[GeorgeB]

I will try to make it more readable.

 

[GeorgeB]

Hope this image reads better.

 

[ksdhart2]

Nope, sorry. Still just as unreadable as before. It might just be quicker and easier to type it out by hand, rather than fiddle with photos that seem to rarely work in the desired manner. If you don't already know it, learning LaTeX code will likely prove helpful. For instance, with LaTeX you can type out expressions like this:

\(\displaystyle \dfrac{3}{5}\)

The LaTeX code for the above is:

[tex]\dfrac{3}{5}[/tex]

A guide I like to refer to occasionally, which lists many many symbols and functions one can use is located here.

 

[stapel]

Hope this image reads better.

Sorry, no; we need a new, bigger image. Re-posting the same image isn't helping.

Or, you could just type out the original expression, and maybe also type out your working. Thank you!

 

[GeorgeB]

OK...I am very sorry about not getting the image correct. This is my first post so I will work on that.

I finally understand this equation as a result of trying to get it right on this forum so that is good and I thank everyone for their patience. Just to tie things up this was the problem:

SIMPLIFY THE FOLLOWING RATIONAL EXPRESSION.

48-3n^2 / n^2+n-20

WHICH VALUES OF N MAKE THE EXPRESSION UNDEFINED?

The stated answer is:

THE SIMPLIFIED FORM OF THE EXPRESSION IS 3(4+n) / n+5

THE VALUES OF n THAT MAKE THE EXPRESSION UNDEFINED ARE n=4 and n = -5

Thanks for all of your patience on this.

 

[stapel]

SIMPLIFY THE FOLLOWING RATIONAL EXPRESSION.

48-3n^2 / n^2+n-20

Lacking grouping symbols, what you have posted means the following:

. . . . .\(\displaystyle 48\, -\, \dfrac{3n^2}{n^2}\, +\, n\, -\, 20\)

From the grainy image, I'm pretty sure you meant this instead:

. . . . .\(\displaystyle \dfrac{48\, -\, 3n^2}{n^2\, +\, n\, -\, 20}\)

(To learn how to use standard web-safe formatting, please review this article.)

WHICH VALUES OF N MAKE THE EXPRESSION UNDEFINED?

The stated answer is:

THE SIMPLIFIED FORM OF THE EXPRESSION IS 3(4+n) / n+5

What steps were required to reach this simplification? (Hint: It involved factoring quadratics and factoring differences of squares.) What hole was "removed" by the cancellation of the common factor? (here)

THE VALUES OF n THAT MAKE THE EXPRESSION UNDEFINED ARE n=4 and n = -5

The one restriction is obvious, "by observation". The other restriction is hidden, due to the cancellation. (here)

 

[ksdhart2]

Erm... I'm sorry, but now I'm even more confused, because the "simplified" version is not equal to the original equation. You can graph them both yourself and you'll see that they're not the same.

 

[GeorgeB]

Thanks for all of your help...I did get this explained to me so all is good.