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

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

Solve for a (complex solution)

$$a=3$$

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

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,x^{2}-1.

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

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

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

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

$$xa+a-x+1=2x+4$$

Add x to both sides.

$$xa+a+1=2x+4+x$$

Combine 2x and x to get 3x.

$$xa+a+1=3x+4$$

Subtract 1 from both sides.

$$xa+a=3x+4-1$$

Subtract 1 from 4 to get 3.

$$xa+a=3x+3$$

Combine all terms containing a.

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

Divide both sides by x+1.

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

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

$$a=\frac{3x+3}{x+1}$$

Divide 3+3x by x+1.

$$a=3$$

Solve for x (complex solution)

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

$$a=3$$

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

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

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

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

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

$$xa+a-x+1=2x+4$$

Subtract 2x from both sides.

$$xa+a-x+1-2x=4$$

Combine -x and -2x to get -3x.

$$xa+a-3x+1=4$$

Subtract a from both sides.

$$xa-3x+1=4-a$$

Subtract 1 from both sides.

$$xa-3x=4-a-1$$

Subtract 1 from 4 to get 3.

$$xa-3x=3-a$$

Combine all terms containing x.

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

Divide both sides by -3+a.

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

Dividing by -3+a undoes the multiplication by -3+a.

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

Divide 3-a by -3+a.

$$x=-1$$

Variable x cannot be equal to -1.

$$x\in \emptyset$$

Solve for a

$$a=3$$

$$|x|\neq 1$$

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,x^{2}-1.

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

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

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

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

$$xa+a-x+1=2x+4$$

Add x to both sides.

$$xa+a+1=2x+4+x$$

Combine 2x and x to get 3x.

$$xa+a+1=3x+4$$

Subtract 1 from both sides.

$$xa+a=3x+4-1$$

Subtract 1 from 4 to get 3.

$$xa+a=3x+3$$

Combine all terms containing a.

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

Divide both sides by x+1.

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

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

$$a=\frac{3x+3}{x+1}$$

Divide 3+3x by x+1.

$$a=3$$

Solve for x

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

$$a=3$$

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

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

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

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

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

$$xa+a-x+1=2x+4$$

Subtract 2x from both sides.

$$xa+a-x+1-2x=4$$

Combine -x and -2x to get -3x.

$$xa+a-3x+1=4$$

Subtract a from both sides.

$$xa-3x+1=4-a$$

Subtract 1 from both sides.

$$xa-3x=4-a-1$$

Subtract 1 from 4 to get 3.

$$xa-3x=3-a$$

Combine all terms containing x.

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

Divide both sides by -3+a.

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

Dividing by -3+a undoes the multiplication by -3+a.

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

Divide 3-a by -3+a.

$$x=-1$$

Variable x cannot be equal to -1.

$$x\in \emptyset$$