Solve 4/3+4/x-4=x+20/3x-12

$$\frac { 4 } { 3 } + \frac { 4 } { x - 4 } = \frac { x + 20 } { 3 x - 12 }$$

Solve for x

$$x=8$$

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 3,x-4,3x-12.

$$3\left(x-4\right)\times \frac{4}{3}+3\times 4=x+20$$

Use the distributive property to multiply 3 by x-4.

$$\left(3x-12\right)\times \frac{4}{3}+3\times 4=x+20$$

Use the distributive property to multiply 3x-12 by \frac{4}{3}.

$$4x-16+3\times 4=x+20$$

Multiply 3 and 4 to get 12.

$$4x-16+12=x+20$$

Add -16 and 12 to get -4.

$$4x-4=x+20$$

Subtract x from both sides.

$$4x-4-x=20$$

Combine 4x and -x to get 3x.

$$3x-4=20$$

Add 4 to both sides.

$$3x=20+4$$

Add 20 and 4 to get 24.

$$3x=24$$

Divide both sides by 3.

$$x=\frac{24}{3}$$

Divide 24 by 3 to get 8.

$$x=8$$