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

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

Solve for x

$$x=\frac{1}{5}=0.2$$

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 3\left(x-1\right)\left(x+1\right), the least common multiple of x+1,3x-3.

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

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

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

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

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

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

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

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

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

Subtract 3 from 2 to get -1.

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

Subtract 2x from both sides.

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

Combine -3x and -2x to get -5x.

$$3x^{2}-5x=-1+3x^{2}$$

Subtract 3x^{2} from both sides.

$$3x^{2}-5x-3x^{2}=-1$$

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

$$-5x=-1$$

Divide both sides by -5.

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

Fraction \frac{-1}{-5} can be simplified to \frac{1}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{5}$$