Solve 1/6+1/x=1/12/5

$$\frac { 1 } { 6 } + \frac { 1 } { x } = \frac { 1 } { 12 / 5 }$$

Solve for x

$$x=4$$

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 6x, the least common multiple of 6,x.

$$6x\times \frac{1}{6}+6=6x\times \frac{1}{\frac{12}{5}}$$

Cancel out 6 and 6.

$$x+6=6x\times \frac{1}{\frac{12}{5}}$$

Divide 1 by \frac{12}{5} by multiplying 1 by the reciprocal of \frac{12}{5}.

$$x+6=6x\times 1\times \frac{5}{12}$$

Multiply 1 and \frac{5}{12} to get \frac{5}{12}.

$$x+6=6x\times \frac{5}{12}$$

Express 6\times \frac{5}{12} as a single fraction.

$$x+6=\frac{6\times 5}{12}x$$

Multiply 6 and 5 to get 30.

$$x+6=\frac{30}{12}x$$

Reduce the fraction \frac{30}{12} to lowest terms by extracting and canceling out 6.

$$x+6=\frac{5}{2}x$$

Subtract \frac{5}{2}x from both sides.

$$x+6-\frac{5}{2}x=0$$

Combine x and -\frac{5}{2}x to get -\frac{3}{2}x.

$$-\frac{3}{2}x+6=0$$

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{3}{2}x=-6$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

$$x=-6\left(-\frac{2}{3}\right)$$

Express -6\left(-\frac{2}{3}\right) as a single fraction.

$$x=\frac{-6\left(-2\right)}{3}$$

Multiply -6 and -2 to get 12.

$$x=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x=4$$