How do you factor ((x+3)^(1/2)) - ((x+3)^(3/2)?

Question

I know the answer, I need to know how it's done--I don't understand the answer at all!

Thanks.

I probably should have mentioned that the book says the answer is -((x+3)^(1/2))(X+2).

Maybe I'm typing it in wrong? It is quantity x+3 to the 1/2 and then that times quantity x+3 to the 3/2.

I typed it in the same way I did in the title into an online factoring program and got the same answer as the third poster.

Is the book wrong?

Answer 1

To make it easier to see, use another variable.

Let u = x + 3.

Then you're trying to factor:

u^(1/2) - u^(3/2)

The common factor is u^(1/2), so factor that out:

u^(1/2) [ 1 - u ]

(Can you see how that works? u^(1/2)u^1 = u^(1/2 + 1) = u^(3/2).)

Now go back to the xs:

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

Or maybe to make it look nicer:

-(x + 2)√(x + 3)

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yeah, pretty sure the book is missing a minus sign.

Answer 2

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

Answer 3

start by taking out the (x+3):
[(x+3)^(1/2)]*[1-(x+3)]