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Math Help - Find Function g

  1. #1
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    Find Function g

    Given f(x) = 1/x and (f/g) (x) = (x + 1)/( x^2 - x), find the function g.
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    Quote Originally Posted by blueridge View Post
    Given f(x) = 1/x and (f/g) (x) = (x + 1)/( x^2 - x), find the function g.
    I assume that (f/g)(x) = \frac{f(x)}{g(x)} = \frac{1}{xg(x)} = \frac{x+1}{x^2-x}

    Rewrite,
    \frac{1}{xg(x)} = \frac{x+1}{x(x-1)}
    Take reciprocals,
    xg(x) = \frac{x(x-1)}{x+1}
    Thus,
    g(x) = \frac{x-1}{x+1}
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  3. #3
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    ok

    You said "thus" but did not complete your statement.
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  4. #4
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    Quote Originally Posted by blueridge View Post
    You said "thus" but did not complete your statement.
    Notice the LHS has x as a product and the RHS has x as a product. Thus, I divided the x's from the two sides. And was let with g(x) what I was looking for.
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