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Math Help - Simplifying Expression, help

  1. #1
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    Simplifying Expression, help

    I need step by step help on simplifying this expression:

    (2x^2 - 18) / (4x^8) divided by (6x^2 + 6x - 36) / (8x^4)
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  2. #2
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    Hello, jenbones!

    \text{Simplify: }\;\dfrac{2x^2 - 18}{4x^8} \div \dfrac{6x^2 + 6x - 36}{8x^4}

    First, "invert and multiply":

    . . \dfrac{2x^2-18}{4x^8} \cdot \dfrac{8x^4}{6x^2+6x-36}


    The first numerator factors:

    . . 2x^2-18 \;=\;2(x^2-9) \;=\;2(x-3)(x+3)


    The second denominator factors:

    . . 6x^2 + 6x - 36 \;=\;6(x^2+x-6) \;=\;6(x-2)(x+3)


    The problem becomes: . \dfrac{2(x-3)(x+3)}{4x^8} \cdot \dfrac{8x^4}{6(x-2)(x+3)}


    Can you finish up?

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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by jenbones View Post
    I need step by step help on simplifying this expression:

    (2x^2 - 18) / (4x^8) divided by (6x^2 + 6x - 36) / (8x^4)


    Hi jenbones,

    \dfrac{2x^2-18}{4x^8} \div \dfrac{6x^2+6x-36}{8x^4}=

    \dfrac{2(x^2-9)}{4x^8} \times \dfrac{8x^4}{6(x^2+x-6)}=

    \dfrac{2(x+3)(x-3)}{4x^8} \times \dfrac{8x^4}{6(x+3)(x-2)}=

    \dfrac{16x^4(x+3)(x-3)}{24x^8(x+3)(x-2)}=


    \dfrac{2(x-3)}{3x^4(x-2)}


    Late again!
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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, jenbones!


    First, "invert and multiply":

    . . \dfrac{2x^2-18}{4x^8} \cdot \dfrac{8x^4}{6x^2+6x-36}


    The first numerator factors:

    . . 2x^2-18 \;=\;2(x^2-9) \;=\;2(x-3)(x+3)


    The second denominator factors:

    . . 6x^2 + 6x - 36 \;=\;6(x^2+x-6) \;=\;6(x-2)(x+3)


    The problem becomes: . \dfrac{2(x-3)(x+3)}{4x^8} \cdot \dfrac{8x^4}{6(x-2)(x+3)}


    Can you finish up?

    Yes, I can thank you
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