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Factoring

PaperStSoap

New member
Jun 26, 2012
9
Simplify

(x+3)1/2 - (x+3)3/2

i honestly am so lost on this one

how i approached it was

(x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)]

but again, i have no idea what I'm doing.
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,043
Simplify

(x+3)1/2 - (x+3)3/2

i honestly am so lost on this one

how i approached it was

(x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)]

but again, i have no idea what I'm doing.
You're doing it correctly.

Now you need to use the fact that \(\displaystyle \frac{x^a}{x^b}=x^{a-b}\). Here you have the same term, (x+3), both the numerator and denominator so you can subtract the powers. What do you get once you do that?
 

PaperStSoap

New member
Jun 26, 2012
9
You're doing it correctly.

Now you need to use the fact that \(\displaystyle \frac{x^a}{x^b}=x^{a-b}\). Here you have the same term, (x+3), both the numerator and denominator so you can subtract the powers. What do you get once you do that?
well 3/2 minus 1/2 equals 1. so wouldnt [(x+3)/(x+3)] = 1?
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,043
well 3/2 minus 1/2 equals 1. so wouldnt [(x+3)/(x+3)] = 1?
Almost. You do get 1, but that's the new power. So you get
\(\displaystyle \frac{(x+3)^{\frac{3}{2}}}{(x+3)^{\frac{1}{2}}}=(x+3)^{\frac{2}{2}}=(x+3)^1=(x+3)\)
 

PaperStSoap

New member
Jun 26, 2012
9
so that would come out to

(x+3)^1/2 [1 - (x + 3)]
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,043

PaperStSoap

New member
Jun 26, 2012
9
(x+3)^1/2[-x+2] ?
 

Jameson

Administrator
Staff member
Jan 26, 2012
4,043

PaperStSoap

New member
Jun 26, 2012
9
man i cant believe i messed that one up
so final answer is
(x+3)^1/2 (-x-2)