Solve k/1-x=3/1+x

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

Solve for k (complex solution)

$$k=-\frac{3\left(x-1\right)}{x+1}$$

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

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.

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

To find the opposite of 1+x, find the opposite of each term.

$$\left(-1-x\right)k=\left(x-1\right)\times 3$$

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

$$-k-xk=\left(x-1\right)\times 3$$

Use the distributive property to multiply x-1 by 3.

$$-k-xk=3x-3$$

Combine all terms containing k.

$$\left(-1-x\right)k=3x-3$$

The equation is in standard form.

$$\left(-x-1\right)k=3x-3$$

Divide both sides by -1-x.

$$\frac{\left(-x-1\right)k}{-x-1}=\frac{3x-3}{-x-1}$$

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

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

Divide -3+3x by -1-x.

$$k=-\frac{3\left(x-1\right)}{x+1}$$

Solve for k

$$k=-\frac{3\left(x-1\right)}{x+1}$$

$$|x|\neq 1$$

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.

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

To find the opposite of 1+x, find the opposite of each term.

$$\left(-1-x\right)k=\left(x-1\right)\times 3$$

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

$$-k-xk=\left(x-1\right)\times 3$$

Use the distributive property to multiply x-1 by 3.

$$-k-xk=3x-3$$

Combine all terms containing k.

$$\left(-1-x\right)k=3x-3$$

The equation is in standard form.

$$\left(-x-1\right)k=3x-3$$

Divide both sides by -x-1.

$$\frac{\left(-x-1\right)k}{-x-1}=\frac{3x-3}{-x-1}$$

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

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

Divide -3+3x by -x-1.

$$k=-\frac{3\left(x-1\right)}{x+1}$$

Solve for x

$$x=-\frac{k-3}{k+3}$$

$$k\neq 0\text{ and }k\neq -3$$

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.

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

To find the opposite of 1+x, find the opposite of each term.

$$\left(-1-x\right)k=\left(x-1\right)\times 3$$

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

$$-k-xk=\left(x-1\right)\times 3$$

Use the distributive property to multiply x-1 by 3.

$$-k-xk=3x-3$$

Subtract 3x from both sides.

$$-k-xk-3x=-3$$

Add k to both sides.

$$-xk-3x=-3+k$$

Combine all terms containing x.

$$\left(-k-3\right)x=-3+k$$

The equation is in standard form.

$$\left(-k-3\right)x=k-3$$

Divide both sides by -k-3.

$$\frac{\left(-k-3\right)x}{-k-3}=\frac{k-3}{-k-3}$$

Dividing by -k-3 undoes the multiplication by -k-3.

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

Divide k-3 by -k-3.

$$x=-\frac{k-3}{k+3}$$

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

$$x=-\frac{k-3}{k+3}\text{, }x\neq -1\text{ and }x\neq 1$$