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Math Help - factoring

  1. #1
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    factoring

    I have two problems that i need help with.

    the first is (5x/y)/(9z)

    would you multiply by 1/9z? to get 5x/9yz?

    the second is 7x^-1 + 7y^-1
    6(x + y)^-1 so this one you would want to put every thing under one so the negatives would cancel out then the lcd is 7x 7y? I'm really confused on this problem.
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  2. #2
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    Re: factoring

    Your answer to the first question is correct.

    For the second one \displaystyle \frac{7x^{-1}+7y^{-1}}{6(x+y)^{-1}} = \frac{(7x^{-1}+7y^{-1})(x+y)}{6}

    Now expand the numerator, what do you get?
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  3. #3
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    Re: factoring

    by expand do you mean like foil? or combine the like terms and add the exponents so it would be 7x+7y/6?
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  4. #4
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    Re: factoring

    Quote Originally Posted by hannah2329 View Post
    by expand do you mean like foil?
    Yes, then combine any like terms.


    Quote Originally Posted by hannah2329 View Post
    so it would be 7x+7y/6?
    I don't think its that, how did you get that?
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  5. #5
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    Re: factoring

    i don't know, I'm confused. if you multiply and add the exponents wouldn't it be -1+1?
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  6. #6
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    Re: factoring

    so it would be 0. is the answer 1/6? I'm really lost.
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  7. #7
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    Re: factoring

    \displaystyle  \frac{(7x^{-1}+7y^{-1})(x+y)}{6}  = \frac{7x^{-1}x+7x^{-1}y+7y^{-1}x+7y^{-1}y}{6}= \frac{7+7x^{-1}y+7y^{-1}x+7}{6}= \dots
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  8. #8
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    Re: factoring

    i got that far but i don't know how to get rid of the negatives
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  9. #9
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    Re: factoring

    You can factor out 7 in the numerator. Do you have to get rid of the negatives?
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  10. #10
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    Re: factoring

    yea i have to get rid of the negatives so 7(y/x+x/y+2)/6
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  11. #11
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    Re: factoring

    That's better...
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  12. #12
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    Re: factoring

    i put that in and it wasn't right. is there any way to simplify it further?
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  13. #13
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    Re: factoring

    Quote Originally Posted by hannah2329 View Post
    i put that in and it wasn't right. is there any way to simplify it further?
    You can simplify even further and get :

    \frac{7(x+y)^2}{6xy}
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