Solve x+1/x-1=3x+5/3x-2

$$\frac { x + 1 } { x - 1 } = \frac { 3 x + 5 } { 3 x - 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values \frac{2}{3},1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(3x-2\right), the least common multiple of x-1,3x-2.

$$\left(3x-2\right)\left(x+1\right)=\left(x-1\right)\left(3x+5\right)$$

Use the distributive property to multiply 3x-2 by x+1 and combine like terms.

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

Use the distributive property to multiply x-1 by 3x+5 and combine like terms.

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

Subtract 3x^{2} from both sides.

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

Combine 3x^{2} and -3x^{2} to get 0.

$$x-2=2x-5$$

Subtract 2x from both sides.

$$x-2-2x=-5$$

Combine x and -2x to get -x.

$$-x-2=-5$$

Add 2 to both sides.

$$-x=-5+2$$

Add -5 and 2 to get -3.

$$-x=-3$$

Multiply both sides by -1.

$$x=3$$