If \(\left(x+\dfrac{1}{x}\right):\left(x-\dfrac{1}{x}\right)=5:4\), then find the value of x.
1.25 (x- 1/x) = (x + 1/x) in ratio 5:4 one side is 1.25 the other 1.25*4 = 5
x - 1/x = 1.25x + 1.25/x
.25x = 2.25/x
.25x^2 = 2.25
.5x = 1.5
x = 3
+36916 
