# Homework Help: Factoring problem

1. Jun 19, 2012

### Government$1. The problem statement, all variables and given/known data http://alphacapitalist.com/wp-content/uploads/2012/06/factoringproblem.jpg [Broken] 2. Relevant equations / 3. The attempt at a solution I tried factoring this but it seems to me that author has made an error somewhere. Either solution to this problem is not 1/a-1 or there is error in the problem itself. Why? Well i tried putting a=2 and using author's solution i should get 1 but when i put it in the problem get 1.714. Any thoughts? Last edited by a moderator: May 6, 2017 2. Jun 19, 2012 ### HallsofIvy I have no clue what this is supposed to be. For one thing it is too small and too dark to read well. Also, there is a symbol between the last two terms inside the parentheses that looks like ":". What does that mean? 3. Jun 19, 2012 ### Government$

":" means divided.

Maybe this will help:
(3/a-1 - 3a^2+3a+3/a^2-1 : a^4 - a/a^3 +1) * a - a^2/3

And the solution is 1/a-1

4. Jun 19, 2012

I did it and got $\frac{1}{a-1}$.

First I would get rid of the divide then remember that $a^3 -1 = (a-1)(a^2 + a + 1)$

See how you go from there.

5. Jun 19, 2012

### Government$Where do you see a^3 - 1? 6. Jun 19, 2012 ### micromass Why don't you start by showing what you tried to solve the problem?? 7. Jun 19, 2012 ### Ray Vickson That is incorrect: the answer is 1/(a-1), not (1/a)-1, which is what your written expression means. RGV 8. Jun 19, 2012 ### Bread18 $a^4 - a = a(a^3 - 1)$ 9. Jun 20, 2012 ### Government$

Here is my stab at it:

($\frac{3}{a-1} - \frac{3a^2+3a+3}{a^2-1} : \frac{a^4-a}{a^3+1}$) * $\frac{a-a^2}{3}$ = ($\frac{-3a^2}{a^2-1}$ * $\frac{(a+1)(a^2-a+1)}{a(a-1)(a^2+a+1)}$) * $\frac{a-a^2}{3}$ = $\frac{-a(a^2-a+1)(a-a^2)}{(a-1)(a-1)(a^2+a+1)}$ = $\frac{a^2(a^2-a+1)}{(a-1)(a^2+a+1)}$ = $\frac{a^4 - a^3 + a^2}{a^3 - 1}$

10. Jun 20, 2012

What did you do to get to ($\frac{-3a^2}{a^2-1}$ * $\frac{(a+1)(a^2-a+1)}{a(a-1)(a^2+a+1)}$)?

11. Jun 20, 2012

### Government\$

OMFG i made such a stuipid mistake. Instead of first dividing i have subtracted and of course i couldnt get a right solution. I have caluclated and gotten a rght solution.
Thank you all!

12. Jun 21, 2012

### dimension10

The symbol ":" has been used in 2 different contexts here. Assuming it means $\divide$, try cancelling out the "a-1".

Last edited by a moderator: May 6, 2017