Solve 3/x+1-3/x-1=3(x-1)-3(x+1)/(x+1)(x-1)

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

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus -1,1$$

Solution Steps

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,x-1,\left(x+1\right)\left(x-1\right).

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

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

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

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

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

To find the opposite of 3x+3, find the opposite of each term.

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

Combine 3x and -3x to get 0.

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

Subtract 3 from -3 to get -6.

$$-6=3\left(x-1\right)-3\left(x+1\right)$$

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

$$-6=3x-3-3\left(x+1\right)$$

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

$$-6=3x-3-3x-3$$

Combine 3x and -3x to get 0.

$$-6=-3-3$$

Subtract 3 from -3 to get -6.

$$-6=-6$$

Compare -6 and -6.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

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

$$x\in \mathrm{C}\setminus -1,1$$

Solve for x

$$x\in \mathrm{R}\setminus -1,1$$

Solution Steps

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,x-1,\left(x+1\right)\left(x-1\right).

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

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

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

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

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

To find the opposite of 3x+3, find the opposite of each term.

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

Combine 3x and -3x to get 0.

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

Subtract 3 from -3 to get -6.

$$-6=3\left(x-1\right)-3\left(x+1\right)$$

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

$$-6=3x-3-3\left(x+1\right)$$

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

$$-6=3x-3-3x-3$$

Combine 3x and -3x to get 0.

$$-6=-3-3$$

Subtract 3 from -3 to get -6.

$$-6=-6$$

Compare -6 and -6.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

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

$$x\in \mathrm{R}\setminus -1,1$$