Solve a/x-1-2/x+1=4/(x-1)(x+1)

$$\frac { a } { x - 1 } - \frac { 2 } { x + 1 } = \frac { 4 } { ( x - 1 ) ( x + 1 ) }$$

Solve for a (complex solution)

$$a=2$$

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

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

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

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

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

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

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

To find the opposite of 2x-2, find the opposite of each term.

$$xa+a-2x+2=4$$

Add 2x to both sides.

$$xa+a+2=4+2x$$

Subtract 2 from both sides.

$$xa+a=4+2x-2$$

Subtract 2 from 4 to get 2.

$$xa+a=2+2x$$

Combine all terms containing a.

$$\left(x+1\right)a=2+2x$$

The equation is in standard form.

$$\left(x+1\right)a=2x+2$$

Divide both sides by x+1.

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

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

$$a=\frac{2x+2}{x+1}$$

Divide 2+2x by x+1.

$$a=2$$

Solve for x (complex solution)

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

$$a=2$$

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

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

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

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

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

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

To find the opposite of 2x-2, find the opposite of each term.

$$xa+a-2x+2=4$$

Subtract a from both sides.

$$xa-2x+2=4-a$$

Subtract 2 from both sides.

$$xa-2x=4-a-2$$

Subtract 2 from 4 to get 2.

$$xa-2x=2-a$$

Combine all terms containing x.

$$\left(a-2\right)x=2-a$$

Divide both sides by -2+a.

$$\frac{\left(a-2\right)x}{a-2}=\frac{2-a}{a-2}$$

Dividing by -2+a undoes the multiplication by -2+a.

$$x=\frac{2-a}{a-2}$$

Divide 2-a by -2+a.

$$x=-1$$

Variable x cannot be equal to -1.

$$x\in \emptyset$$

Solve for a

$$a=2$$

$$|x|\neq 1$$

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

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

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

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

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

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

To find the opposite of 2x-2, find the opposite of each term.

$$xa+a-2x+2=4$$

Add 2x to both sides.

$$xa+a+2=4+2x$$

Subtract 2 from both sides.

$$xa+a=4+2x-2$$

Subtract 2 from 4 to get 2.

$$xa+a=2+2x$$

Combine all terms containing a.

$$\left(x+1\right)a=2+2x$$

The equation is in standard form.

$$\left(x+1\right)a=2x+2$$

Divide both sides by x+1.

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

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

$$a=\frac{2x+2}{x+1}$$

Divide 2+2x by x+1.

$$a=2$$

Solve for x

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

$$a=2$$

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

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

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

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

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

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

To find the opposite of 2x-2, find the opposite of each term.

$$xa+a-2x+2=4$$

Subtract a from both sides.

$$xa-2x+2=4-a$$

Subtract 2 from both sides.

$$xa-2x=4-a-2$$

Subtract 2 from 4 to get 2.

$$xa-2x=2-a$$

Combine all terms containing x.

$$\left(a-2\right)x=2-a$$

Divide both sides by -2+a.

$$\frac{\left(a-2\right)x}{a-2}=\frac{2-a}{a-2}$$

Dividing by -2+a undoes the multiplication by -2+a.

$$x=\frac{2-a}{a-2}$$

Divide 2-a by -2+a.

$$x=-1$$

Variable x cannot be equal to -1.

$$x\in \emptyset$$