Factoring

PaperStSoap

New member
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

Staff member
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
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

Staff member
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
so that would come out to

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

Jameson

Staff member
so that would come out to

(x+3)^1/2 [1 - (x + 3)]
Exactly. Now just simplify [1-(x+3)] and you're done.

PaperStSoap

New member
(x+3)^1/2[-x+2] ?

Jameson

$$\displaystyle 1-(x+3)=1-x-3=-x-2$$ so final answer is
$$\displaystyle (-x-2)\sqrt{x+3}$$