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

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

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

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

Is my attempt CORRECT please check it but if not please write your answers in steps...

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

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

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

Is my attempt CORRECT please check it but if not please write your answers in steps...

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

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

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

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

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

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

3. Just a little more

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

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

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

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

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

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

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

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