Solve 1/x=1/12+1/2.4

$$\frac{ 1 }{ x } = \frac{ 1 }{ 12 } + \frac{ 1 }{ 2.4 }$$

Solve for x

$$x=2$$

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,12.

$$12=12x\times \frac{1}{12}+12x\times \frac{1}{2.4}$$

Cancel out 12 and 12.

$$12=x+12x\times \frac{1}{2.4}$$

Expand \frac{1}{2.4} by multiplying both numerator and the denominator by 10.

$$12=x+12x\times \frac{10}{24}$$

Reduce the fraction \frac{10}{24} to lowest terms by extracting and canceling out 2.

$$12=x+12x\times \frac{5}{12}$$

Cancel out 12 and 12.

$$12=x+5x$$

Combine x and 5x to get 6x.

$$12=6x$$

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

$$6x=12$$

Divide both sides by 6.

$$x=\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$x=2$$