1/[(3^0.5)-1]=[(3^0.5)+1]/2
Both sides equal 1.36603... but I don't know the steps to get from the first equation to the second.
The sides are just "expressions" since, by definition, the sides do not include the "equals" sign. So I think you're asking how to go from the expression on the one side of the equation to the expression on the other side of the equation. You've verified that both sides evaluate to the same decimal form, so you "believe" the equation, but you're foggy on the arithmetic.
First, I'll state what I'm seeing the equation to be:
. . . . .\(\displaystyle \dfrac{1}{3^{0.5}\, -\, 1}\, =\, \dfrac{3^{0.5}\, +\, 1}{2}\)
Second, let's convert the left-hand side to radical notation:
. . . . .\(\displaystyle \dfrac{1}{\sqrt{3}\, -\, 1}\)
Third, recall that it's considered "improper" (at this stage of your studies) to have a radical in the denominator. To get rid of the radical, you'll need to multiply, top and bottom, by the conjugate of the radical expression:
. . . . .\(\displaystyle \left(\dfrac{1}{\sqrt{3}\, -\, 1}\right)\, \left(\dfrac{\sqrt{3}\, +\, 1}{\sqrt{3}\, +\, 1}\right)\)
What do you get when you do the computations?
