Solve 1/x^2=1/t-1

$$\frac { 1 } { x ^ { 2 } } = \frac { 1 } { t - 1 }$$

Solve for t

$$t=x^{2}+1$$

$$x\neq 0$$

Solution Steps

Variable t cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by \left(t-1\right)x^{2}, the least common multiple of x^{2},t-1.

$$t-1=x^{2}$$

Add 1 to both sides.

$$t=x^{2}+1$$

Variable t cannot be equal to 1.

$$t=x^{2}+1\text{, }t\neq 1$$

Solve for x (complex solution)

$$x=-\sqrt{t-1}$$

$$x=\sqrt{t-1}\text{, }t\neq 1$$

Solve for x

$$x=\sqrt{t-1}$$

$$x=-\sqrt{t-1}\text{, }t>1$$