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Thread: rational equation and rearraging formaul

  1. #1
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    Question rational equation and rearraging formaul

    hey guys! my first post!

    i needed some help

    how do you so the following rational equation

    (x-1)^2 / x-2 = 9 / 2

    and also

    how do you make y the subject of the formula when

    y+2 / y+1 = x

    i been trying to solve this all morning!

    anyways guys if you can help please do..

    .. oh yeah and a very good site for MATHS help

    http://www.mathtutor.ac.uk/

    http://www.mathcentre.ac.uk/

    hope you find them useful
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dadon
    how do you so the following rational equation

    (x-1)^2 / x-2 = 9 / 2
    $\displaystyle \frac{(x-1)^2}{x-2}=\frac{9}{2}$

    No factors cancel, so assuming x is not equal to 2, we can multiply both sides by (x-2) and multiply both sides by 2:

    $\displaystyle 2(x-1)^2=9(x-2)$
    $\displaystyle 2x^2-4x+2=9x-18$
    $\displaystyle 2x^2-13x+20=0$
    $\displaystyle (2x-5)(x-4)=0$

    So $\displaystyle 2x-5=0$ or $\displaystyle x-4=0$

    Finally: x = 5/2 or x = 4. Quick check: Neither of these says x = 2, so we're okay.

    -Dan
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by dadon
    hey guys! my first post!

    i needed some help

    how do you so the following rational equation

    (x-1)^2 / x-2 = 9 / 2
    $\displaystyle
    \frac{(x-1)^2} { x-2} = \frac{9}{ 2}
    $

    so multiplying both sides by $\displaystyle x-2$:

    $\displaystyle
    (x-1)^2 = \frac{9}{ 2} (x-2)
    $,

    expanding the square:

    $\displaystyle
    x^2-2x+1 = \frac{9}{ 2} (x-2)
    $,

    bringing everthing over to the LHS

    $\displaystyle
    x^2-\frac{13}{2}x+10 = 0
    $.

    Which can now be solved using the quadratic formula.

    RonL
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dadon
    how do you make y the subject of the formula when

    y+2 / y+1 = x
    $\displaystyle \frac{y+2}{y+1}=x$

    Multiplying both sides by (y+1):

    $\displaystyle y+2 = x(y+1)$
    $\displaystyle y+2=xy+x$
    $\displaystyle y-xy=x-2$
    $\displaystyle y(1-x)=x-2$
    $\displaystyle y = \frac{x-2}{1-x}$

    This is sufficient, though some people might prefer the following form, given that x-1 = -(1-x):
    $\displaystyle y =- \frac{x-2}{x-1}$

    -Dan
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    re:

    thanks guys exactly what i needed!
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