Solve 3/x-4=4/3x-12-2

$$\frac { 3 } { x - 4 } = \frac { 4 } { 3 x - 12 } - 2$$

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 4 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-4\right), the least common multiple of x-4,3x-12.

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

Multiply 3 and 3 to get 9.

$$9=4+3\left(x-4\right)\left(-2\right)$$

Multiply 3 and -2 to get -6.

$$9=4-6\left(x-4\right)$$

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

$$9=4-6x+24$$

Add 4 and 24 to get 28.

$$9=28-6x$$

Swap sides so that all variable terms are on the left hand side.

$$28-6x=9$$

Subtract 28 from both sides.

$$-6x=9-28$$

Subtract 28 from 9 to get -19.

$$-6x=-19$$

Divide both sides by -6.

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

Fraction \frac{-19}{-6} can be simplified to \frac{19}{6} by removing the negative sign from both the numerator and the denominator.

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