Solve 2/1+x-k/1-x=-6/x^2-1

$$\frac { 2 } { 1 + x } - \frac { k } { 1 - x } = \frac { - 6 } { x ^ { 2 } - 1 }$$

Solve for k (complex solution)

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

$$x\neq -1\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of 1+x,1-x,x^{2}-1.

$$\left(x-1\right)\times 2-\left(-\left(1+x\right)k\right)=-6$$

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

$$2x-2-\left(-\left(1+x\right)k\right)=-6$$

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

$$2x-2-\left(-1-x\right)k=-6$$

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

$$2x-2-\left(-k-xk\right)=-6$$

To find the opposite of -k-xk, find the opposite of each term.

$$2x-2+k+xk=-6$$

Subtract 2x from both sides.

$$-2+k+xk=-6-2x$$

Add 2 to both sides.

$$k+xk=-6-2x+2$$

Add -6 and 2 to get -4.

$$k+xk=-4-2x$$

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by 1+x.

$$\frac{\left(x+1\right)k}{x+1}=\frac{-2x-4}{x+1}$$

Dividing by 1+x undoes the multiplication by 1+x.

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

Divide -4-2x by 1+x.

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

Solve for k

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

$$|x|\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of 1+x,1-x,x^{2}-1.

$$\left(x-1\right)\times 2-\left(-\left(1+x\right)k\right)=-6$$

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

$$2x-2-\left(-\left(1+x\right)k\right)=-6$$

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

$$2x-2-\left(-1-x\right)k=-6$$

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

$$2x-2-\left(-k-xk\right)=-6$$

To find the opposite of -k-xk, find the opposite of each term.

$$2x-2+k+xk=-6$$

Subtract 2x from both sides.

$$-2+k+xk=-6-2x$$

Add 2 to both sides.

$$k+xk=-6-2x+2$$

Add -6 and 2 to get -4.

$$k+xk=-4-2x$$

Combine all terms containing k.

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

The equation is in standard form.

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

Divide both sides by 1+x.

$$\frac{\left(x+1\right)k}{x+1}=\frac{-2x-4}{x+1}$$

Dividing by 1+x undoes the multiplication by 1+x.

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

Divide -4-2x by 1+x.

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

Solve for x

$$x=-\frac{k+4}{k+2}$$

$$k\neq -2\text{ and }k\neq -3$$

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

$$\left(x-1\right)\times 2-\left(-\left(1+x\right)k\right)=-6$$

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

$$2x-2-\left(-\left(1+x\right)k\right)=-6$$

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

$$2x-2-\left(-1-x\right)k=-6$$

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

$$2x-2-\left(-k-xk\right)=-6$$

To find the opposite of -k-xk, find the opposite of each term.

$$2x-2+k+xk=-6$$

Add 2 to both sides.

$$2x+k+xk=-6+2$$

Add -6 and 2 to get -4.

$$2x+k+xk=-4$$

Subtract k from both sides.

$$2x+xk=-4-k$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by k+2.

$$\frac{\left(k+2\right)x}{k+2}=\frac{-k-4}{k+2}$$

Dividing by k+2 undoes the multiplication by k+2.

$$x=\frac{-k-4}{k+2}$$

Divide -4-k by k+2.

$$x=-\frac{k+4}{k+2}$$

Variable x cannot be equal to any of the values -1,1.

$$x=-\frac{k+4}{k+2}\text{, }x\neq -1\text{ and }x\neq 1$$