# 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
$$\displaystyle (-x-2)\sqrt{x+3}$$