Here,

\(\sqrt{\frac x{1-x}}+\sqrt{\frac{1-x}x}=\frac{13}6\)
Or, \(\frac{\sqrt x}{\sqrt{1-x}}+\sqrt{\frac{1-x}x}=\frac{13}6\)
Or, \(\frac{\left(\sqrt x^2\right)+\left(\sqrt{1-x}\right)^2}{\sqrt{1-x\;}\sqrt x}=\frac{13}6\)
Or,\(\frac{\displaystyle x+\left(1-x\right)}{\sqrt{x-x^2}}=\frac{13}6\)
Or,\(\frac{\displaystyle x+1-x}{\sqrt{x-x^2}}=\frac{13}6\)
Or,\(\frac{\displaystyle1}{\sqrt{x-x^2}}=\frac{13}6\)
Squaring both sides, we get
\(\left(\frac{\displaystyle1}{\sqrt{x-x^2}}\right)^2=\left(\frac{13}6\right)^2\)
Or,\(\frac1{x-x^2}=\frac{169}{36}\)
Or,36=169(x-x²)
Or,36=169x-169x²
Or,169² - 169x+36=0
Or,169² - (117 - 52)x + 36 = 0
Or,169² - 117x - 52x + 36 = 0
Or,13x(13x-9)-4(13x-9) = 0
Or,(13x-9) (13x-4) = 0

Either, 13x-9=0
Or,13x=9
Or,\(x=\frac9{13}\)


Or, 13x - 4 = 0
Or, 13x=4
Or, \(x=\frac4{13}\)