Solve 4/x^2-1+x+2/1-x=-1

$$\frac { 4 } { x ^ { 2 } - 1 } + \frac { x + 2 } { 1 - x } = - 1$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

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

$$4-\left(1+x\right)\left(x+2\right)=-\left(x-1\right)\left(x+1\right)$$

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

$$4+\left(-1-x\right)\left(x+2\right)=-\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply -1-x by x+2 and combine like terms.

$$4-3x-2-x^{2}=-\left(x-1\right)\left(x+1\right)$$

Subtract 2 from 4 to get 2.

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

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

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

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

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

Add x^{2} to both sides.

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

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

$$2-3x=1$$

Subtract 2 from both sides.

$$-3x=1-2$$

Subtract 2 from 1 to get -1.

$$-3x=-1$$

Divide both sides by -3.

$$x=\frac{-1}{-3}$$

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

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