SOLUTION: Need a lesson on how to factor an expression with fractional exponets. Probably not searching the right thing on youtube. I typed each twice because the formula plottting system i

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Question 541125: Need a lesson on how to factor an expression with fractional exponets. Probably not searching the right thing on youtube.
I typed each twice because the formula plottting system is cutting off the top of the fractions on my screen.

Book gives the example:
3x^(3/2) - 9x^(1/2) + 6x^(-1/2)
= 3x^(-1/2) *(x^2-3x+2)
= 3x^(-1/2) (x-1)(x+2)

I am just not getting much from that example
I have a few problems in the book with the final answer:
x^(-3/2) + 2x^(-1/2) + x^(1/2)
x%5E%28-3%2F2%29+%2B+2x%5E%28-1%2F2%29+%2B+x%5E%281%2F2%29
The final answer is:
x^(-3/2) * (x+1)^2
x%5E%28-3%2F2%29+%2A+%28x%2B1%29%5E2
Can you show me detailed steps?
Another problem is:
2x^(1/3)*(x-2)^(2/3) - 5x^(4/3)(x-2)^(-1/3)
2x%5E%281%2F3%29%2A%28x-2%29%5E%282%2F3%29+-+5x%5E%284%2F3%29%28x-2%29%5E%28-1%2F3%29
The final answer is:
x^(1/3) *(x-2)^(-1/3)* (-3x-4)
x%5E%281%2F3%29+%2A%28x-2%29%5E%28-1%2F3%29%2A+%28-3x-4%29
Thanks in advace for your help!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
3x^(3/2) - 9x^(1/2) + 6x^(-1/2)
greatest common factor of 3,-9, and 6 : 3
gcf of x^(3/2),x^(1/2), x^(-1/2): x^(-1/2); the lowest power is always the gcf
= 3x^(-1/2)[x^2 -3x + 2)
---
= 3x^(-1/2)(x-2)(x-1)
======================================


I have a few problems in the book with the final answer:
x^(-3/2) + 2x^(-1/2) + x^(1/2)
---
gcf is lowest power: x^(-3/2)
---
= (x^(-3/2))(1 + 2x + x^2)
---
= x^(-3/2)(1+x)(1+x)
========================================
Another problem is:
2x^(1/3)*(x-2)^(2/3) - 5x^(4/3)(x-2)^(-1/3)
---
gcf is x^(1/3)*(x-2)^(-1/3)
---
= [x^(1/3)*(x-2)^(-1/3)]
---
= [x^(1/3)*(x-2)^(-1/3)]
=====
Cheers,
Stan H.