Assuming the usual carelessness with parentheses,
7√(x/(1-x)) + 9√((1-x)/x) =15
49x/(1-x) + 2*7*9 + 81(1-x)/x = 225
[49x^2 + 81(1-x)^2]/(x(1-x)) + 126 = 225
130x^2 - 162x + 81 = 99x(1-x)
Now finish it off
7√(x/1-x) + 9√(1-x/x) =15
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