Having trouble with algebraic fractions.

[yunaray89]

I don't understand this type of problem very well, and am having trouble getting started with those that haven't been explained by the teacher already. Here are the instructions and examples (in italics); sorry, but there are quite a lot. Fractions will be represented by the division symbol.


ADDITION RULE FOR FRACTIONS
a/c + b/c = a+b/c

SUBTRACTION RULE FOR FRACTIONS
a/c - b/c = a-b/c

<u>example one</u>
3c/16 + 5c/16 = 3c+5c/16 = 8c/16 = c/2

<u>example two</u>
2/x-3 + 7/3-x = 2/x-3 - 7/x-3 = 2-7/x-3 = -5/x-3

<u>example three</u>
a/4 - 5+12a/18 = a*9/4*9 - 2(5+12a)/18*2 = 9a-2(5+12a)/36 = - 5(3a+2)/36

<u>example four</u>
3/2x - 1/8x^2 = 3*4x/2x*4x - 1/8x^2 = 12x/8x^2 - 1/8x^2 = 12x-1/8x^2

<u>example five</u>
a-3/a^2-2a - a-4/a^2-4 = a-3/a(a-2) - a-4/(a-2)(a+2) = (a+3)(a+2)/a(a-2)(a+2) - a(a-4)/a(a-2)(a+2) = a^2-a-6-a^2+4a/a(a-2)(a+2) = 3a-6/a(a-2)(a+2) = 3(a-2)/a(a-2)(a+2) = 3/a(a+2)


Now we're done with that. Whew, lots of numbers to type. Okay... on to my question.

The problem is 2n/n^3-5n^2 + 2/n^2+5n.

I don't really get where to go from here. I know I need to find the LCD, but I'm not sure how on this one. Also, after that I'm pretty much lost as well... I've never been much of the fraction type.

To anyone who can help, I greatly appreciate it.

 

[jonboy]

Hi, yunaray89!


.....Assuming this is what you mean...

\(\displaystyle \L \;\frac{2n}{n^{3}\,-\,5n^{2}}\,+\,\frac{3}{n^{2}\,+\,5n}\,=\,?\)

Factor out \(\displaystyle n\) on the left:\(\displaystyle \L \;\frac{n(2)}{n(n^{2}\,-\,5n)}\,+\,\frac{3}{n^{2}\,+\,5n}\,=\,?\)

The \(\displaystyle n's\) on the left outside the parenthesis cancel, giving you:\(\displaystyle \L \;\frac{2}{n^{2}\,-\,5n\,}+\,\frac{3}{n^{2}\,+\,5n}\,=\,?\)

Our cd will be:\(\displaystyle \L \;(n^{2}\,-\,5n)\,(n^{2}\,+\,5n)\)

Which gives us: \(\displaystyle \L \;\frac{2 n^{2}\,+\,10n}{(n^{2}\,-\,5n)\,(n^{2}\,+\,5n)}\,+\,\frac{3n^{2}\,-\,15n}{(n^{2}\,-\,5n)\,(n^{2}\,+\,5n)}\,=\,?\)


We have a common denominator, use "addition rules for fractions and like terms". :idea:

 

[yunaray89]

Thanks so much! This helps tons; I think I can continue now.

 

[Denis]

The problem is 2n/n^3-5n^2 + 2/n^2+5n.

That needs BRACKETS; like this:
2n / (n^3 - 5n^2) + 2 / (n^2 + 5n)

Simplify the left term:
2n / (n^3 - 5n^2) = 2n / n(n^2 - 5n) = 2 / (n^2 - 5n)
So we now have:
2 / (n^2 - 5n) + 2 / (n^2 + 5n)

= [2 (n^2 + 5n) + 2 (n^2 - 5n)] / [(n^2 - 5n) (n^2 + 5n)]

= (2n^2 + 10n + 2n^2 - 10n) / (n^4 - 25n^2)

= 4n^2 / [n^2(n^2 - 25)]

= 4 / (n^2 - 25)

= 4 / [(n+5)(n-5)]