MHB Simplifying (x+3)1/2 - (x+3)3/2 Expression

[PaperStSoap]

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]

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 [math]\frac{x^a}{x^b}=x^{a-b}[/math]. 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]

You're doing it correctly.

Now you need to use the fact that [math]\frac{x^a}{x^b}=x^{a-b}[/math]. 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 wouldn't [(x+3)/(x+3)] = 1?

 

[Jameson]

well 3/2 minus 1/2 equals 1. so wouldn't [(x+3)/(x+3)] = 1?

Almost. You do get 1, but that's the new power. So you get
[math]\frac{(x+3)^{\frac{3}{2}}}{(x+3)^{\frac{1}{2}}}=(x+3)^{\frac{2}{2}}=(x+3)^1=(x+3)[/math]

 

[PaperStSoap]

so that would come out to

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

 

[Jameson]

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]

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

 

[Jameson]

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

[math]1-(x+3)=1-x-3=-x-2[/math] so final answer is

[math](-x-2)\sqrt{x+3}[/math]

 

[PaperStSoap]

man i can't believe i messed that one up
so final answer is
(x+3)^1/2 (-x-2)