Question 16456
You do need to be careful when you write: t = 1 - x^2/x^2 when you really mean: t = (1 - x^2)/x^2. But here's how you would do it.

{{{x^2 = 1/(t+1)}}} Multiply both sides by (t+1)
{{{(t+1)x^2 = 1}}} Divide both sides by x^2
{{{t+1 = 1/x^2}}} Subtract 1 from both sides.
{{{t = (1/x^2) - 1}}} Simplify.
{{{t = (1 - x^2)/x^2}}}