# Thread: Find the sum or difference in the lowest term?

1. ## Find the sum or difference in the lowest term?

1) $\displaystyle \frac{a+1}{a^3} - \frac{a+2}{a^2} +\frac{a+3}{a}$

Attempt:
$\displaystyle \frac{a^4-a^3+2a^5+a^6}{a^6}$

Thank you for your help and for taking the time to read my question

2. Originally Posted by mj.alawami
1) $\displaystyle \frac{a+1}{a^3} - \frac{a+2}{a^2} +\frac{a+3}{a}$

Attempt:
$\displaystyle \frac{a^4-a^3+2a^5+a^6}{a^6}$

Thank you for your help and for taking the time to read my question
$\displaystyle a^3$ is the LCD ...

$\displaystyle \frac{a+1}{a^3} - \frac{a+2}{a^2} +\frac{a+3}{a}$

$\displaystyle \frac{a+1}{a^3} - \frac{a(a+2)}{a^3} +\frac{a^2(a+3)}{a^3}$

$\displaystyle \frac{(a+1)-a(a+2)+a^2(a+3)}{a^3} =$

$\displaystyle \frac{a+1-a^2-2a+a^3+3a^2}{a^3} =$

$\displaystyle \frac{a^3+2a^2-a+1}{a^3}$

3. Just a little more

$\displaystyle = \frac{a^3(a -1+2a^2 + a^3 )}{a^3 \times a^3}$

$\displaystyle =\frac{(a -1+2a^2 + a^3 )}{a^3}$

4. Originally Posted by skeeter
$\displaystyle a^3$ is the LCD ...

$\displaystyle \frac{a+1}{a^3} - \frac{a+2}{a^2} +\frac{a+3}{a}$

$\displaystyle \frac{a+1}{a^3} - \frac{a(a+2)}{a^3} +\frac{a^2(a+3)}{a^3}$

$\displaystyle \frac{(a+1)-a(a+2)+a^2(a+3)}{a^3} =$

$\displaystyle \frac{a+1-a^2-2a+a^3+3a^2}{a^3} =$

$\displaystyle \frac{a^3+2a^2-a+1}{a^3}$
Thanks aloots