# Thread: HELP! Fractions, variables, exponents, THE WORKS!!

1. ## HELP! Fractions, variables, exponents, THE WORKS!!

(2n/n^3-5n^2) + (2/n^2+ 5n)

Please help, i have been trying to figure this out but i cant seem to finsih it! THANKS SO MUCH

2. Hello, beachchick984!

$\displaystyle \frac{2n}{n^3-5n^2} + \frac{2}{n^2+ 5n}$

Factor the denominators: .$\displaystyle \underbrace{\frac{n}{n^2(n-5)}}_{\text{Reduce}} + \frac{2}{n(n+5)}$

And we have: .$\displaystyle \frac{2}{n(n-5)} + \frac{2}{n(n+5)}$

Get a common denominator: . $\displaystyle {\color{blue}\frac{n+5}{n+5}}\cdot\frac{2}{n(n-5)} \;+ \;{\color{blue}\frac{n-5}{n-5}}\cdot\frac{2}{n(n+5)}$

. . $\displaystyle = \;\frac{2(n+5) + 2(n-5)}{n(n-5)(n+5)} \;= \;\frac{2n+10+2n-10}{n(n-5)(n+5)} \;=\;\frac{4n}{n(n-5)(n+5)}$ .$\displaystyle =\;\boxed{\frac{4}{(n-5)(n+5)}}$

3. Originally Posted by Soroban
Hello, beachchick984!

Factor the denominators: .$\displaystyle \underbrace{\frac{n}{n^2(n-5)}}_{\text{Reduce}} + \frac{2}{n(n+5)}$

And we have: .$\displaystyle \frac{2}{n(n-5)} + \frac{2}{n(n+5)}$

Get a common denominator: . $\displaystyle {\color{blue}\frac{n+5}{n+5}}\cdot\frac{2}{n(n-5)} \;+ \;{\color{blue}\frac{n-5}{n-5}}\cdot\frac{2}{n(n+5)}$

. . $\displaystyle = \;\frac{2(n+5) + 2(n-5)}{n(n-5)(n+5)} \;= \;\frac{2n+10+2n-10}{n(n-5)(n+5)} \;=\;\frac{4n}{n(n-5)(n+5)}$ .$\displaystyle =\;\boxed{\frac{4}{(n-5)(n+5)}}$

THANK YOU SOOOOOOOOO MUCH!!!

4. Originally Posted by Soroban
Hello, beachchick984!

Factor the denominators: .$\displaystyle \underbrace{\frac{n}{n^2(n-5)}}_{\text{Reduce}} + \frac{2}{n(n+5)}$

And we have: .$\displaystyle \frac{2}{n(n-5)} + \frac{2}{n(n+5)}$

Get a common denominator: . $\displaystyle {\color{blue}\frac{n+5}{n+5}}\cdot\frac{2}{n(n-5)} \;+ \;{\color{blue}\frac{n-5}{n-5}}\cdot\frac{2}{n(n+5)}$

. . $\displaystyle = \;\frac{2(n+5) + 2(n-5)}{n(n-5)(n+5)} \;= \;\frac{2n+10+2n-10}{n(n-5)(n+5)} \;=\;\frac{4n}{n(n-5)(n+5)}$ .$\displaystyle =\;\boxed{\frac{4}{(n-5)(n+5)}}$
one question when you get .$\displaystyle =\;\boxed{\frac{4}{(n-5)(n+5)}}$ do you combine or finish the problem or just leave (n-5)(n+5) as is? thanks again