Solve 5x-4/x-1+2/3x-3-2x-7/2x-2=3

$$\frac { 5 x - 4 } { x - 1 } + \frac { 2 } { 3 x - 3 } - \frac { 2 x - 7 } { 2 x - 2 } = 3$$

Solve for x

$$x = -\frac{19}{6} = -3\frac{1}{6} \approx -3.166666667$$

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 6\left(x-1\right), the least common multiple of x-1,3x-3,2x-2.

$$6\left(5x-4\right)+2\times 2-3\left(2x-7\right)=18\left(x-1\right)$$

Use the distributive property to multiply 6 by 5x-4.

$$30x-24+2\times 2-3\left(2x-7\right)=18\left(x-1\right)$$

Multiply 2 and 2 to get 4.

$$30x-24+4-3\left(2x-7\right)=18\left(x-1\right)$$

Add -24 and 4 to get -20.

$$30x-20-3\left(2x-7\right)=18\left(x-1\right)$$

Use the distributive property to multiply -3 by 2x-7.

$$30x-20-6x+21=18\left(x-1\right)$$

Combine 30x and -6x to get 24x.

$$24x-20+21=18\left(x-1\right)$$

Add -20 and 21 to get 1.

$$24x+1=18\left(x-1\right)$$

Use the distributive property to multiply 18 by x-1.

$$24x+1=18x-18$$

Subtract 18x from both sides.

$$24x+1-18x=-18$$

Combine 24x and -18x to get 6x.

$$6x+1=-18$$

Subtract 1 from both sides.

$$6x=-18-1$$

Subtract 1 from -18 to get -19.

$$6x=-19$$

Divide both sides by 6.

$$x=\frac{-19}{6}$$

Fraction \frac{-19}{6} can be rewritten as -\frac{19}{6} by extracting the negative sign.

$$x=-\frac{19}{6}$$