Solve 1/1-x^2=1

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

Solve for x

$$x=0$$

Steps by Finding Square Root

Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(-x-1\right).

$$1=\left(x-1\right)\left(-x-1\right)$$

Use the distributive property to multiply x-1 by -x-1 and combine like terms.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 1 from both sides.

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

Subtract 1 from 1 to get 0.

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

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(-x-1\right).

$$1=\left(x-1\right)\left(-x-1\right)$$

Use the distributive property to multiply x-1 by -x-1 and combine like terms.

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 1 from both sides.

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

Subtract 1 from 1 to get 0.

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

Divide both sides by -1. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$