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

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

Solve for x

$$x=2$$

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.

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

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

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

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

$$3x-3=x^{2}+x+\left(x-1\right)\left(x+1\right)\left(-1\right)$$

Use the distributive property to multiply x-1 by x+1 and combine like terms.

$$3x-3=x^{2}+x+\left(x^{2}-1\right)\left(-1\right)$$

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

$$3x-3=x^{2}+x-x^{2}+1$$

Combine x^{2} and -x^{2} to get 0.

$$3x-3=x+1$$

Subtract x from both sides.

$$3x-3-x=1$$

Combine 3x and -x to get 2x.

$$2x-3=1$$

Add 3 to both sides.

$$2x=1+3$$

Add 1 and 3 to get 4.

$$2x=4$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$x=2$$