Subtraction of rational expression...algebra?

Question

5k/4k-8 - k/k+2 Can someone help me solve this .......do not understand how to get commom demoninator

Answer 1

The common denominator is simply the product of the two denominators: in this case, (4k-8)(k+2)

So this yields 5k(k+2) - k(4k-8) = 5k^2 + 10k - 4k^2 + 8k = k^2+18k in the numerator and (4k-8)(k+2) in the denominator

Answer 2

It would help if you had some parenthesis in there, it's hard to tell what your denomitors are...
Do you mean
(5k/(4k-8)) - (k/(k+2))?
Generally, the common denominator is the product of all the factors in your denominators. If they're relatively prime, you'd simply multiply the denominators together. Even if they're not relatively prime you could get away with this although it would give you a common denominator larger than necessary.
In this case, assuming that I've read it right, the first term's denominator factors as 4(k-2) and the second term's denominator does not factor. So your common denominator is 4(k+2)(k-2) which you could write as 4(k^2-4) although I wouldn't recommend it at this point, becuase your next step is to convert all terms to common denominator. You do this by inspecting the denominators you have, comparing them to the common denominator, and then multiply the top and bottom by "what's missing". (I notice at this point that Jason has a common denominator that looks different from mine, but it's really the same if you multiply it out and rearrange the terms) Ok, here we go...
5k/(4k-8) = 5k/(4(k-2)) is missing a (k + 2) so multiply the top and bottom by (k+2) and you get
5k(k+2)/(4(k-2)(k+2))
Similarly, k/(k+2) is missing a 4(k-2) so multiply top and bottom by this and you get
(4k(k-2))/(4(k+2)(k-2))
Now you have a common denominator so you can combine terms on top:
(5k(k+2) - 4k(k-2)) = 5k^2 + 10k - 4k^2 + 8k =
k^2 + 18k (that looks a little funny, I may have made a mistake in there. Work it out yourself and see what you get.)
This doesn't appear to have any common factors with the denominator so if it's correct go ahead and put it over the denominator and you're done.
(k^2 + 18k)/(4(k^2 - 4))
Note : it may look like you can cancel something in there but you can't cancel things that are added and subtracted, you can only cancel things that are multiplied and divided.
I admit, this is a little hard to read, with this limited online text editor. There are some good online explanations on this and many other math topics. To find them, just put subject tutorial in your search window. For example, I'll put rational expressions tutorial in my search window for you and see what comes up...
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut10_addrat.htm
(lots more but this one seemed good for a start. You might want to look at the one right before this one, about simplifying rational expressions, as well.)

Answer 3

The most simplified result is:

k (k + 18) / [4 (k -2) (k + 2)], or equivalently:

k (k + 18) / [4 (k^2 - 4)].

Here's how. I first insert parentheses in your original expression, to avoid possible confusion in interpretation. (Please study for the benefit of both yourself and your readers, in future) :

5k/(4k-8) - k/(k+2) = [5k (k+ 2) - 4 k (k - 2)] / [4 (k - 2) (k + 2)].

Explanation: What did I do after inserting the parentheses in your original expression? I noticed that the first denominator was 4 (k - 2); then I made a least common mutiple of [4 (k - 2) (k + 2)] in the denominator, simply by multiplying both denominators together, in this case.

[Should there be a common factor already in the denominators, that itself can be extracted first before multiplying the remaining terms. In this case, there was no such common factor, so simply multiplying the exhibited denominators together was the simplest thing to do ! ]

The next step was to multiply the two original numerators by the necessary factors implied, in order to bring both numerator expressions over that common denominator. Then, as shown explicitly in the line of algebra above, I subtracted the resulting numerators, as a preliminary step before final simplification of that numerator. That's the next step.

Simplifying the numerator, that is now:

5 k^2 + 10 k - 4 k^2 + 8 k = k^2 + 18 k = k (k + 18).

So the full, simplified result is:

k (k + 18) / [4 (k - 2) (k + 2)].

It's a matter of taste whether you now combine the two parentheses in the denominator to write this whole thing as:

k (k + 18) / [4 (k^2 - 4)].

I hope this has helped you.

Live long and prosper.

Answer 4

((5k)/(4k - 8)) - (k/(k + 2))
((5k)/(4(k - 2))) - (k/(k + 2))

Multiply everything by 4(k - 2)(k + 2)

(5k(k + 2) - 4k(k - 2))/(4(k - 2)(k + 2))
(5k^2 + 10k - 4k^2 + 8k)/(4(k - 2)(k + 2))
(k^2 + 18k)/(4(k^2 - 4))
(k^2 + 18k)/(4k^2 - 16)

Answer 5

(5k/4k-8)-(k/k+2)
={5k/4(k-2)} - (k/k+2)
={5k(k+2)}-{k*4(k-2)}/4(k+2)(k-2)
[ 4(k+2)(k-2) is the LCD]
=(5k^2+10k)-(4k^2-8k)/4(k^2-4)
(k^2+18k)/4k^2-16