anonymous
  • anonymous
Hey everyone back to school can someone help with this problem (x+2)^-1/2 (2x+4)+(x+2)^3/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Are you supposed to simplify the problem?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
ok look at the parentheses on the left. Can you pull out any common factors?

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anonymous
  • anonymous
oh oops I mean one in the middle.
anonymous
  • anonymous
ok but what do I do with those darn exponents. LOL
anonymous
  • anonymous
just a sec, I'm working it out. will explain as soon as I'm done.
anonymous
  • anonymous
ok here goes: Pulling out the common 2, you get: 2(x+2)(x+2)^-1/2 + (x+2)^3/2 right?
anonymous
  • anonymous
ok
anonymous
  • anonymous
So now can you see any terms that can be pulled out of the addition?
anonymous
  • anonymous
actually first: can you simplify the left side of the addition at all?
anonymous
  • anonymous
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
anonymous
  • anonymous
notice that both have a base of (x+2). What does that mean about the exponents?
anonymous
  • anonymous
yea I'm sorry not a clue. Ugh Christmas break ruined me
anonymous
  • anonymous
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.....
anonymous
  • anonymous
I am so sorry and feel like an idiot right now. I get that the exponents are multiplied
anonymous
  • anonymous
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?
anonymous
  • anonymous
ok oops thats what I meant. But didn't the (-) exponent go to the denominator
anonymous
  • anonymous
you can do that too, but in this case it's simply easier to add up the exponents, eliminating the denominator altogether.
anonymous
  • anonymous
ok then what do I do?
anonymous
  • anonymous
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.
anonymous
  • anonymous
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.
anonymous
  • anonymous
so my final answer should be (x+2)^1/2 + (x+4)
anonymous
  • anonymous
yup! :)
anonymous
  • anonymous
oh wait no. They're multiplied, not added.
anonymous
  • anonymous
ok thanks (feel like an idiot) lol
anonymous
  • anonymous
no problem!

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