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    by eliminating x and y from these equations
     \frac{1}{x}+\frac{1}{y}= 1,   x +y = a  ,   \frac{y}{x} = m
    where a\neq 0 , obtain a relation between m and a. Given that a is real, determine the ranges of values of a for which m is real.

    I managed to get   a = \frac{(m+1)^2}{m}
    but the question as to give the ranges of a.
    from what i learn for instance if  f(x) = x^2 + 3x + 4 you can be asked to find the range of values of x.
    but for this question i got   a = \frac{(m+1)^2}{m} .
    As a result, it is difficult for me to find the range of values of a as a is not where m is.
    How do i rearrange it to have m as the dependent variable in order to find the range of a

    thank you

    Rearrange for m, you will need to solve a quadratic in m, but be careful not to get rid of half of the curve when you do.
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