Question

Hey everyone back to school can someone help with this problem (x+2)^-1/2 (2x+4)+(x+2)^3/2

Answer 1

Are you supposed to simplify the problem?

Answer 2

Yes

Answer 3

ok look at the parentheses on the left. Can you pull out any common factors?

Answer 4

oh oops I mean one in the middle.

Answer 5

ok but what do I do with those darn exponents. LOL

Answer 6

just a sec, I'm working it out. will explain as soon as I'm done.

Answer 7

ok here goes:
Pulling out the common 2, you get: 2(x+2)(x+2)^-1/2 + (x+2)^3/2 right?

Answer 8

ok

Answer 9

So now can you see any terms that can be pulled out of the addition?

Answer 10

actually first: can you simplify the left side of the addition at all?

Answer 11

the (x+2)^-1/2 goes to the bottom and the 2 can be factored from the (2x+4) leaving 2(x+2) over (x+2)^1/2

Answer 12

notice that both have a base of (x+2). What does that mean about the exponents?

Answer 13

yea I'm sorry not a clue. Ugh Christmas break ruined me

Answer 14

When the bases are equal, 2 multiplied exponents can be added. for example: 2^2 * 2^3 = 2^5. In this case, the base is (x+2) and the exponents are 1 and -1/2. soo.....

Answer 15

I am so sorry and feel like an idiot right now. I get that the exponents are multiplied

Answer 16

exponents should be added. In this case 1-1/2 = 1/2. As a result:
you get 2(x+2)^1/2 + (x+2)^3/2 right?

Answer 17

ok oops thats what I meant. But didn't the (-) exponent go to the denominator

Answer 18

you can do that too, but in this case it's simply easier to add up the exponents, eliminating the denominator altogether.

Answer 19

ok then what do I do?

Answer 20

Now you have a common term of (x+2)^1/2 that you can pull out of both terms in the addition. It's like the opposite of the distributive property.

Answer 21

Doing that, you get (x+2)^1/2 times(2 + x + 2), which simplifies to (x+4)(x+2)^1/2. and you're done.

Answer 22

so my final answer should be (x+2)^1/2 + (x+4)

Answer 23

yup! :)

Answer 24

oh wait no. They're multiplied, not added.

Answer 25

ok thanks (feel like an idiot) lol

Answer 26

no problem!