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Thread: How to solve this rational expression?

  1. #1
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    How to solve this rational expression?

    x^2-8x+15
    ___________
    2x^2-7x-15

    So far I've got for the numerator:
    (x-3)(x-5)

    What goes below, and how did you do it? Thank you.
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  2. #2
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    Re: How to solve this rational expression?

    Quote Originally Posted by Ashir View Post
    x^2-8x+15
    ___________
    2x^2-7x-15

    So far I've got for the numerator:
    (x-3)(x-5)

    What goes below, and how did you do it? Thank you.
    2x^2-7x-15=(2x+3)(x-5)
    Last edited by Plato; Jul 30th 2012 at 02:04 PM.
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  3. #3
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    Re: How to solve this rational expression?

    Thank you. How did you get that?
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  4. #4
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    Re: How to solve this rational expression?

    Quote Originally Posted by Ashir View Post
    How did you get that?
    Practice, practice, practice.
    Multiply the answer out to see how it works.
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  5. #5
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    Re: How to solve this rational expression?

    I don't understand; what method did you use to arrive at that answer?
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  6. #6
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    Re: How to solve this rational expression?

    Quote Originally Posted by Ashir View Post
    I don't understand; what method did you use to arrive at that answer?
    There is no method. I just looked at and knew the answer. I have done enough of these to have that skill.
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  7. #7
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    Re: How to solve this rational expression?

    (2x+2)(x-5) =
    2x^2-10x+2x-10
    2x^2-8x-10
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    Re: How to solve this rational expression?

    Quote Originally Posted by Ashir View Post
    (2x+2)(x-5) =
    2x^2-10x+2x-10
    2x^2-8x-10
    But it is (2x+3)(x-5)
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  9. #9
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    Re: How to solve this rational expression?

    You posted (2x+2) though?
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  10. #10
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    Re: How to solve this rational expression?

    Quote Originally Posted by Ashir View Post
    x^2-8x+15
    ___________
    2x^2-7x-15

    So far I've got for the numerator:
    (x-3)(x-5)

    What goes below, and how did you do it? Thank you.
    \displaystyle \begin{align*} 2x^2 - 7x - 15 \end{align*}

    Multiply the a and c values to get -30. You need to look for two numbers that multiply to give -30 and add to give -7. They are -10 and 3. So break up the middle value and factorise by grouping.

    \displaystyle \begin{align*} 2x^2 - 7x - 15 &= 2x^2 - 10x + 3x - 15 \\ &= 2x(x - 5) + 3(x - 5) \\ &= (x - 5)(2x + 3) \end{align*}
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  11. #11
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    Re: How to solve this rational expression?

    The most reliable way to factor a quadratic polynomial ax^2+bx+c is by finding its roots using the quadratic formula. If the roots are x_1 and x_2, then ax^2+bx+c=a(x-x_1)(x-x_2).
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  12. #12
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    Re: How to solve this rational expression?

    Quote Originally Posted by Prove It View Post
    \displaystyle \begin{align*} 2x^2 - 7x - 15 \end{align*}

    Multiply the a and c values to get -30. You need to look for two numbers that multiply to give -30 and add to give -7. They are -10 and 3. So break up the middle value and factorise by grouping.

    \displaystyle \begin{align*} 2x^2 - 7x - 15 &= 2x^2 - 10x + 3x - 15 \\ &= 2x(x - 5) + 3(x - 5) \\ &= (x - 5)(2x + 3) \end{align*}
    Got it, thanks.
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