Solve 2x/x-1-2=5/x^2-1

$$\frac { 2 x } { x - 1 } - 2 = \frac { 5 } { x ^ { 2 } - 1 }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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^{2}-1.

$$\left(x+1\right)\times 2x+\left(x-1\right)\left(x+1\right)\left(-2\right)=5$$

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

$$\left(2x+2\right)x+\left(x-1\right)\left(x+1\right)\left(-2\right)=5$$

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

$$2x^{2}+2x+\left(x-1\right)\left(x+1\right)\left(-2\right)=5$$

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

$$2x^{2}+2x+\left(x^{2}-1\right)\left(-2\right)=5$$

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

$$2x^{2}+2x-2x^{2}+2=5$$

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

$$2x+2=5$$

Subtract 2 from both sides.

$$2x=5-2$$

Subtract 2 from 5 to get 3.

$$2x=3$$

Divide both sides by 2.

$$x=\frac{3}{2}$$