Solve 3x-2/x+1=4-x+2/x-1

$$\frac{ 3x-2 }{ x+1 } =4- \frac{ x+2 }{ x-1 }$$

Solve for x

$$x=4$$

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.

$$\left(x-1\right)\left(3x-2\right)=\left(x-1\right)\left(x+1\right)\times 4-\left(x+1\right)\left(x+2\right)$$

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

$$3x^{2}-5x+2=\left(x-1\right)\left(x+1\right)\times 4-\left(x+1\right)\left(x+2\right)$$

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

$$3x^{2}-5x+2=\left(x^{2}-1\right)\times 4-\left(x+1\right)\left(x+2\right)$$

Use the distributive property to multiply x^{2}-1 by 4.

$$3x^{2}-5x+2=4x^{2}-4-\left(x+1\right)\left(x+2\right)$$

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

$$3x^{2}-5x+2=4x^{2}-4-\left(x^{2}+3x+2\right)$$

To find the opposite of x^{2}+3x+2, find the opposite of each term.

$$3x^{2}-5x+2=4x^{2}-4-x^{2}-3x-2$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$3x^{2}-5x+2=3x^{2}-4-3x-2$$

Subtract 2 from -4 to get -6.

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

Subtract 3x^{2} from both sides.

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

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

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

Add 3x to both sides.

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

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

$$-2x+2=-6$$

Subtract 2 from both sides.

$$-2x=-6-2$$

Subtract 2 from -6 to get -8.

$$-2x=-8$$

Divide both sides by -2.

$$x=\frac{-8}{-2}$$

Divide -8 by -2 to get 4.

$$x=4$$