See this page to see the definition of the Golden Ratio (step 1).

Explaination:

In this proof where (1/x) = (x/(1-x)), our goal was to show the exact value of Phi ((1+√5)/2). We used the simple image above to show the ratios. Then we used simple arithmetic of the Quadratic Formula to show the possible values of x. After, we subsituted for x to derive Phi.