Solve x+3/x+1--x+1/1-x=4/x^2-1

$$\frac { x + 3 } { x + 1 } - \frac { - x + 1 } { 1 - x } = \frac { 4 } { x ^ { 2 } - 1 }$$

Solve for x

$$x=3$$

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

$$\left(x-1\right)\left(x+3\right)-\left(-\left(1+x\right)\left(-x+1\right)\right)=4$$

Use the distributive property to multiply x-1 by x+3 and combine like terms.

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

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

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

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

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

Multiply -1 and -1 to get 1.

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

Multiply -1 and -1 to get 1.

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

Multiply x and x to get x^{2}.

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

Combine x and -x to get 0.

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

To find the opposite of -1+x^{2}, find the opposite of each term.

$$x^{2}+2x-3+1-x^{2}=4$$

Add -3 and 1 to get -2.

$$x^{2}+2x-2-x^{2}=4$$

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

$$2x-2=4$$

Add 2 to both sides.

$$2x=4+2$$

Add 4 and 2 to get 6.

$$2x=6$$

Divide both sides by 2.

$$x=\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$x=3$$