Solve 3+2/x^2-1=1/1-x^2

$$3 + \frac { 2 } { x ^ { 2 } - 1 } = \frac { 1 } { 1 - x ^ { 2 } }$$

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), the least common multiple of x^{2}-1,1-x^{2}.

$$\left(x-1\right)\left(x+1\right)\times 3+2=-1$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$\left(x^{2}-1\right)\times 3+2=-1$$

Use the distributive property to multiply x^{2}-1 by 3.

$$3x^{2}-3+2=-1$$

Add -3 and 2 to get -1.

$$3x^{2}-1=-1$$

Add 1 to both sides.

$$3x^{2}=-1+1$$

Add -1 and 1 to get 0.

$$3x^{2}=0$$

Divide both sides by 3. 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), the least common multiple of x^{2}-1,1-x^{2}.

$$\left(x-1\right)\left(x+1\right)\times 3+2=-1$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$\left(x^{2}-1\right)\times 3+2=-1$$

Use the distributive property to multiply x^{2}-1 by 3.

$$3x^{2}-3+2=-1$$

Add -3 and 2 to get -1.

$$3x^{2}-1=-1$$

Add 1 to both sides.

$$3x^{2}-1+1=0$$

Add -1 and 1 to get 0.

$$3x^{2}=0$$

Divide both sides by 3. 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.

$$x=0$$