Solve x+1/x-1=x-5/x-3

$$\frac { x + 1 } { x - 1 } = \frac { x - 5 } { x - 3 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 1,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x-1\right), the least common multiple of x-1,x-3.

$$\left(x-3\right)\left(x+1\right)=\left(x-1\right)\left(x-5\right)$$

Use the distributive property to multiply x-3 by x+1 and combine like terms.

$$x^{2}-2x-3=\left(x-1\right)\left(x-5\right)$$

Use the distributive property to multiply x-1 by x-5 and combine like terms.

$$x^{2}-2x-3=x^{2}-6x+5$$

Subtract x^{2} from both sides.

$$x^{2}-2x-3-x^{2}=-6x+5$$

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

$$-2x-3=-6x+5$$

Add 6x to both sides.

$$-2x-3+6x=5$$

Combine -2x and 6x to get 4x.

$$4x-3=5$$

Add 3 to both sides.

$$4x=5+3$$

Add 5 and 3 to get 8.

$$4x=8$$

Divide both sides by 4.

$$x=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x=2$$