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Thread: How to simplify this expression

  1. #1
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    How to simplify this expression

    How to simplify this expression-picture-10.png


    I let (x+1)=x and (x-3)=y and I got $\displaystyle \frac{2x^4y^2(3x+y)}{x^{10}}$

    where do I go from here?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: How to simplify this expression

    Rewrite the denominator as $\displaystyle x^4 \cdot x^6$ and divide out the factor common to the numerator and denominator.
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  3. #3
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    Re: How to simplify this expression

    Hello, kingsolomonsgrave!

    $\displaystyle \text{Simplify: }\:\frac{6(x+1)^5(x-3)^2 + 2(x+1)^4(x-3)^3}{(x+1)^{10}}$

    I let (x+1)=x and (x-3)=y. . Don't do that!
    Use two "new" variables:
    .$\displaystyle {\color{blue}x + 1 = u,\;x-3 = v}$

    and I got $\displaystyle \frac{2x^4y^2(3x+y)}{x^{10}}$

    where do I go from here?
    You can cancel the x's . . . and back-substitute.

    We have: .$\displaystyle \frac{6(x+1)^5(x-3)^2 + 2(x+1)^4(x-3)^3}{(x+1)^{10}}$

    Factor: . $\displaystyle \frac{2(x+1)^4(x-3)^2\big[3(x+1) + (x-3)\big]}{(x+1)^{10}} $

    Reduce: . $\displaystyle \frac{2(x-3)^2\big[3x+3 + x - 3\big]}{(x+1)^6} $

    Simplify: .$\displaystyle \frac{2(x-3)^2\cdot4x}{(x+1)^6} \;=\;\frac{8x(x-3)^2}{(x+1)^6} $


    Where did this problem come from?
    If it came from an application of the Quotient Rule,
    . . something is drastically wrong.
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