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Math Help - expressing in terms

  1. #1
    one_passerby
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    Question expressing in terms

    I can't seem to get an answer to this question:
    x= a + (1/y) , y= a - (1/z) where a is constant.

    Express z in terms of a and x only

    anyone?
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  2. #2
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    Quote Originally Posted by one_passerby
    I can't seem to get an answer to this question:
    x= a + (1/y) , y= a - (1/z) where a is constant.

    Express z in terms of a and x only

    anyone?
    You are given that,
    x=a+\frac{1}{y} (1)
    y=a-\frac{1}{z} (2)

    Using equation (2) thus,
    z=\frac{1}{a-y}
    Now using equation (1) we get that,
    y=\frac{1}{x-a}.
    Substitute y from (1) into (2),
    z=\frac{1}{a-\frac{1}{x-a}}
    Simplify this complex fraction,
    z=\frac{x-a}{ax-a^2-1}
    Q.E.D.
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