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

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

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x-2\right), the least common multiple of \left(x-2\right)\left(x-4\right),x-2,x-4.

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

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

$$x+3x-12=x-2$$

Combine x and 3x to get 4x.

$$4x-12=x-2$$

Subtract x from both sides.

$$4x-12-x=-2$$

Combine 4x and -x to get 3x.

$$3x-12=-2$$

Add 12 to both sides.

$$3x=-2+12$$

Add -2 and 12 to get 10.

$$3x=10$$

Divide both sides by 3.

$$x=\frac{10}{3}$$