Answer
$x=1$
Work Step by Step
Let
$u=x^{-1}$
$u^2=x^{-2}$
Using the representations above, the given equation becomes:
$$-u^2+2u=1$$
Add $u^2$ and subtract $2$ to both sides of the equation to obtain:
$$-u^2+2u+u^2-2u=1+u^2-2u
\\0=u^2-2u+1$$
Factor the trinomial to obtain:
$$0=(u-1)(u-1)$$
Use the Zero-Factor Property by equating each factor to zero to obtain:
$$u-1=0 \text{ or } u-1=0$$
Solve each equation to obtain:
$$u=1$$
Replacing $u$ with $x^{-1}$ gives:
$$u=1
\\x^{-1} = 1$$
Use the rule $a^{-m} = \dfrac{1}{a^m}$, then cross-multiply to obtain:
$$\dfrac{1}{x} = 1
\\x(1) = 1
\\x=1$$
