Solve 1/x=1/2+1/4+1/12

$$\frac{ 1 }{ x } = \frac{ 1 }{ 2 } + \frac{ 1 }{ 4 } + \frac{ 1 }{ 12 }$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12x, the least common multiple of x,2,4,12.

$$12=12x\times \frac{1}{2}+12x\times \frac{1}{4}+12x\times \frac{1}{12}$$

Multiply 12 and \frac{1}{2} to get \frac{12}{2}.

$$12=\frac{12}{2}x+12x\times \frac{1}{4}+12x\times \frac{1}{12}$$

Divide 12 by 2 to get 6.

$$12=6x+12x\times \frac{1}{4}+12x\times \frac{1}{12}$$

Multiply 12 and \frac{1}{4} to get \frac{12}{4}.

$$12=6x+\frac{12}{4}x+12x\times \frac{1}{12}$$

Divide 12 by 4 to get 3.

$$12=6x+3x+12x\times \frac{1}{12}$$

Combine 6x and 3x to get 9x.

$$12=9x+12x\times \frac{1}{12}$$

Cancel out 12 and 12.

$$12=9x+x$$

Combine 9x and x to get 10x.

$$12=10x$$

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

$$10x=12$$

Divide both sides by 10.

$$x=\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{6}{5}$$