- Thread starter
- #1

#### PaperStSoap

##### New member

- Jun 26, 2012

- 9

(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.

- Thread starter PaperStSoap
- Start date

- Thread starter
- #1

- Jun 26, 2012

- 9

(x+3)

how i approached it was

(x+3)

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

- Admin
- #2

- Jan 26, 2012

- 4,043

You're doing it correctly.

(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.

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?

- Thread starter
- #3

- Jun 26, 2012

- 9

well 3/2 minus 1/2 equals 1. so wouldnt [(x+3)/(x+3)] = 1?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?

- Admin
- #4

- Jan 26, 2012

- 4,043

Almost. You do get 1, but that's the new power. So you getwell 3/2 minus 1/2 equals 1. so wouldnt [(x+3)/(x+3)] = 1?

\(\displaystyle \frac{(x+3)^{\frac{3}{2}}}{(x+3)^{\frac{1}{2}}}=(x+3)^{\frac{2}{2}}=(x+3)^1=(x+3)\)

- Thread starter
- #5

- Jun 26, 2012

- 9

so that would come out to

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

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

- Admin
- #6

- Jan 26, 2012

- 4,043

Exactly. Now just simplify [1-(x+3)] and you're done.so that would come out to

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

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- #7

- Jun 26, 2012

- 9

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

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- #8

- Jan 26, 2012

- 4,043

\(\displaystyle 1-(x+3)=1-x-3=-x-2\) so final answer is(x+3)^1/2[-x+2] ?

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

- Thread starter
- #9

- Jun 26, 2012

- 9

man i cant believe i messed that one up

so final answer is

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

so final answer is

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