Solve 1/x=3/6-x

$$\frac{ 1 }{ x } = \frac{ 3 }{ 6-x }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,6 since division by zero is not defined. Multiply both sides of the equation by x\left(x-6\right), the least common multiple of x,6-x.

$$x-6=-x\times 3$$

Multiply -1 and 3 to get -3.

$$x-6=-3x$$

Add 3x to both sides.

$$x-6+3x=0$$

Combine x and 3x to get 4x.

$$4x-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$4x=6$$

Divide both sides by 4.

$$x=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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