Solve x+1/a+1=3/a-1-3-2a/a^2-1

$$\frac { x + 1 } { a + 1 } = \frac { 3 } { a - 1 } - \frac { 3 - 2 a } { a ^ { 2 } - 1 }$$

Solve for a (complex solution)

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

$$x\neq \frac{3}{2}\text{ and }x\neq 4$$

Steps for Solving Linear Equation

Variable a 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(a-1\right)\left(a+1\right), the least common multiple of a+1,a-1,a^{2}-1.

$$\left(a-1\right)\left(x+1\right)=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=3a+3-\left(3-2a\right)$$

To find the opposite of 3-2a, find the opposite of each term.

$$ax+a-x-1=3a+3-3+2a$$

Subtract 3 from 3 to get 0.

$$ax+a-x-1=3a+2a$$

Combine 3a and 2a to get 5a.

$$ax+a-x-1=5a$$

Subtract 5a from both sides.

$$ax+a-x-1-5a=0$$

Combine a and -5a to get -4a.

$$ax-4a-x-1=0$$

Add x to both sides. Anything plus zero gives itself.

$$ax-4a-1=x$$

Add 1 to both sides.

$$ax-4a=x+1$$

Combine all terms containing a.

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

Divide both sides by -4+x.

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

Dividing by -4+x undoes the multiplication by -4+x.

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

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

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

Solve for x (complex solution)

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

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

Steps for Solving Linear Equation

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

$$\left(a-1\right)\left(x+1\right)=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=3a+3-\left(3-2a\right)$$

To find the opposite of 3-2a, find the opposite of each term.

$$ax+a-x-1=3a+3-3+2a$$

Subtract 3 from 3 to get 0.

$$ax+a-x-1=3a+2a$$

Combine 3a and 2a to get 5a.

$$ax+a-x-1=5a$$

Subtract a from both sides.

$$ax-x-1=5a-a$$

Combine 5a and -a to get 4a.

$$ax-x-1=4a$$

Add 1 to both sides.

$$ax-x=4a+1$$

Combine all terms containing x.

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

Divide both sides by a-1.

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

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

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

Solve for a

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

$$x\neq 4\text{ and }x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Variable a 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(a-1\right)\left(a+1\right), the least common multiple of a+1,a-1,a^{2}-1.

$$\left(a-1\right)\left(x+1\right)=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=3a+3-\left(3-2a\right)$$

To find the opposite of 3-2a, find the opposite of each term.

$$ax+a-x-1=3a+3-3+2a$$

Subtract 3 from 3 to get 0.

$$ax+a-x-1=3a+2a$$

Combine 3a and 2a to get 5a.

$$ax+a-x-1=5a$$

Subtract 5a from both sides.

$$ax+a-x-1-5a=0$$

Combine a and -5a to get -4a.

$$ax-4a-x-1=0$$

Add x to both sides. Anything plus zero gives itself.

$$ax-4a-1=x$$

Add 1 to both sides.

$$ax-4a=x+1$$

Combine all terms containing a.

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

Divide both sides by -4+x.

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

Dividing by -4+x undoes the multiplication by -4+x.

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

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

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

Solve for x

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

$$|a|\neq 1$$

Steps for Solving Linear Equation

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

$$\left(a-1\right)\left(x+1\right)=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=\left(a+1\right)\times 3-\left(3-2a\right)$$

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

$$ax+a-x-1=3a+3-\left(3-2a\right)$$

To find the opposite of 3-2a, find the opposite of each term.

$$ax+a-x-1=3a+3-3+2a$$

Subtract 3 from 3 to get 0.

$$ax+a-x-1=3a+2a$$

Combine 3a and 2a to get 5a.

$$ax+a-x-1=5a$$

Subtract a from both sides.

$$ax-x-1=5a-a$$

Combine 5a and -a to get 4a.

$$ax-x-1=4a$$

Add 1 to both sides.

$$ax-x=4a+1$$

Combine all terms containing x.

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

Divide both sides by a-1.

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

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

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