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

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

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

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

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

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

Combine 3x and 3x to get 6x.

$$6x+2-3=4\left(x-1\right)$$

Subtract 3 from 2 to get -1.

$$6x-1=4\left(x-1\right)$$

Use the distributive property to multiply 4 by x-1.

$$6x-1=4x-4$$

Subtract 4x from both sides.

$$6x-1-4x=-4$$

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

$$2x-1=-4$$

Add 1 to both sides.

$$2x=-4+1$$

Add -4 and 1 to get -3.

$$2x=-3$$

Divide both sides by 2.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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