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

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

Solve for x

$$x=5$$

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.

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

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

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

Use the distributive property to multiply 2x+2 by x.

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

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

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

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

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

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

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

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

$$2x+2=3x-3$$

Subtract 3x from both sides.

$$2x+2-3x=-3$$

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

$$-x+2=-3$$

Subtract 2 from both sides.

$$-x=-3-2$$

Subtract 2 from -3 to get -5.

$$-x=-5$$

Multiply both sides by -1.

$$x=5$$