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

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

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

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 1-x^{2},x-1.

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

Use the distributive property to multiply x+1 by 2.

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

Use the distributive property to multiply -1 by x-1.

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

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

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

Add x^{2} to both sides.

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

Combine -x^{2} and x^{2} to get 0.

$$2x+2=1$$

Subtract 2 from both sides.

$$2x=1-2$$

Subtract 2 from 1 to get -1.

$$2x=-1$$

Divide both sides by 2.

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

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

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