Solve 3/2x-2+5/x+1=4/x-1

$$\frac { 3 } { 2 x - 2 } + \frac { 5 } { x + 1 } = \frac { 4 } { x - 1 }$$

Solve for x

$$x=3$$

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 2\left(x-1\right)\left(x+1\right), the least common multiple of 2x-2,x+1,x-1.

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

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

$$3x+3+\left(2x-2\right)\times 5=\left(2x+2\right)\times 4$$

Use the distributive property to multiply 2x-2 by 5.

$$3x+3+10x-10=\left(2x+2\right)\times 4$$

Combine 3x and 10x to get 13x.

$$13x+3-10=\left(2x+2\right)\times 4$$

Subtract 10 from 3 to get -7.

$$13x-7=\left(2x+2\right)\times 4$$

Use the distributive property to multiply 2x+2 by 4.

$$13x-7=8x+8$$

Subtract 8x from both sides.

$$13x-7-8x=8$$

Combine 13x and -8x to get 5x.

$$5x-7=8$$

Add 7 to both sides.

$$5x=8+7$$

Add 8 and 7 to get 15.

$$5x=15$$

Divide both sides by 5.

$$x=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$x=3$$