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

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

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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.

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

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

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

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

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

Subtract 2 from -1 to get -3.

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

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

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

Use the distributive property to multiply 2x-2 by x.

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

Subtract 2x^{2} from both sides.

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

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

$$-3=-2x$$

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

$$-2x=-3$$

Divide both sides by -2.

$$x=\frac{-3}{-2}$$

Fraction \frac{-3}{-2} can be simplified to \frac{3}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{2}$$