Algebra

SImplify:

(x - 9/x) / (1 + x/3)

and (m^-1 + n^-1) / (m^-3 + n^-3)

I have no idea what to do

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  1. Answer to #2:

    m^4n^2.

    I subtracted the m's and subtracted the m's. It's one of the exponent rules.

    I have NO idea how to do the first question.

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  2. you cant do that, Miley, the m's and n's are separated by an addition sign, so you cant use the quotient of powers rule

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  3. oh okay sry, at least i tried

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  4. for the first one, just multiply them using FOIL
    to get

    x + (x^2)/3 - 9/x - 3

    for the second, use the rule for negative exponents to write

    (1/m + 1/n)/(1/m^3 + 1/n^3)

    finding common denominators and simplifying both top and bottom I got

    (m+n)/mn / (m^3 + n^3)/m^3n^3
    = (m+n)/mn * (m^3n^3)/(m^3 + n^3)
    = m^2n^2(m+n) / (m^3 + n^3)

    the bottom factors to (m+n)(m^2 - mn + n^2)

    so we have
    m^2n^2(m+n) / ((m+n)(m^2 - mn + n^2))
    = m^2n^2 / (m^2 - mn + n^2)

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