Solve \frac{1}{x}-\frac{1}{x^2}=2

Evaluate

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

Multiply both sides of the equation by LCD

(\frac{1}{x} - \frac{1}{x ^{2}}) x^{2} = 2 x^{2}

Simplify the equation

More Steps

x - 1 = 2 x^{2}

Move the expression to the left side

x - 1 - 2 x^{2} = 0

Rewrite in standard form

- 2 x^{2} + x - 1 = 0

Multiply both sides

2 x^{2} - x + 1 = 0

Substitute a= 2,b= - 1 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 2}{2 \times 2}

Simplify the expression

x = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 2}{4}

Simplify the expression

More Steps

x = \frac{1 \pm - 7}{4}

Solution

x \in / R

Alternative Form

No real solution

Solve the equation