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anonymous

  • 2 years ago

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

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  1. anonymous
    • 2 years ago
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    Are you supposed to simplify the problem?

  2. anonymous
    • 2 years ago
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    Yes

  3. anonymous
    • 2 years ago
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    ok look at the parentheses on the left. Can you pull out any common factors?

  4. anonymous
    • 2 years ago
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    oh oops I mean one in the middle.

  5. anonymous
    • 2 years ago
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    ok but what do I do with those darn exponents. LOL

  6. anonymous
    • 2 years ago
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    just a sec, I'm working it out. will explain as soon as I'm done.

  7. anonymous
    • 2 years ago
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    ok here goes: Pulling out the common 2, you get: 2(x+2)(x+2)^-1/2 + (x+2)^3/2 right?

  8. anonymous
    • 2 years ago
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    ok

  9. anonymous
    • 2 years ago
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    So now can you see any terms that can be pulled out of the addition?

  10. anonymous
    • 2 years ago
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    actually first: can you simplify the left side of the addition at all?

  11. anonymous
    • 2 years ago
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    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

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

  13. anonymous
    • 2 years ago
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    yea I'm sorry not a clue. Ugh Christmas break ruined me

  14. anonymous
    • 2 years ago
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    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.....

  15. anonymous
    • 2 years ago
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    I am so sorry and feel like an idiot right now. I get that the exponents are multiplied

  16. anonymous
    • 2 years ago
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    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?

  17. anonymous
    • 2 years ago
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    ok oops thats what I meant. But didn't the (-) exponent go to the denominator

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

  19. anonymous
    • 2 years ago
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    ok then what do I do?

  20. anonymous
    • 2 years ago
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    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.

  21. anonymous
    • 2 years ago
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    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.

  22. anonymous
    • 2 years ago
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    so my final answer should be (x+2)^1/2 + (x+4)

  23. anonymous
    • 2 years ago
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    yup! :)

  24. anonymous
    • 2 years ago
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    oh wait no. They're multiplied, not added.

  25. anonymous
    • 2 years ago
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    ok thanks (feel like an idiot) lol

  26. anonymous
    • 2 years ago
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    no problem!

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