Solve 1/a+1/b=3/2018

$$\frac { 1 } { a } + \frac { 1 } { b } = \frac { 3 } { 2018 }$$

Solve for a

$$a=-\frac{2018b}{2018-3b}$$

$$b\neq 0\text{ and }b\neq \frac{2018}{3}$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2018ab, the least common multiple of a,b,2018.

$$2018b+2018a=3ab$$

Subtract 3ab from both sides.

$$2018b+2018a-3ab=0$$

Subtract 2018b from both sides. Anything subtracted from zero gives its negation.

$$2018a-3ab=-2018b$$

Combine all terms containing a.

$$\left(2018-3b\right)a=-2018b$$

Divide both sides by 2018-3b.

$$\frac{\left(2018-3b\right)a}{2018-3b}=-\frac{2018b}{2018-3b}$$

Dividing by 2018-3b undoes the multiplication by 2018-3b.

$$a=-\frac{2018b}{2018-3b}$$

Variable a cannot be equal to 0.

$$a=-\frac{2018b}{2018-3b}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{2018a}{2018-3a}$$

$$a\neq 0\text{ and }a\neq \frac{2018}{3}$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2018ab, the least common multiple of a,b,2018.

$$2018b+2018a=3ab$$

Subtract 3ab from both sides.

$$2018b+2018a-3ab=0$$

Subtract 2018a from both sides. Anything subtracted from zero gives its negation.

$$2018b-3ab=-2018a$$

Combine all terms containing b.

$$\left(2018-3a\right)b=-2018a$$

Divide both sides by 2018-3a.

$$\frac{\left(2018-3a\right)b}{2018-3a}=-\frac{2018a}{2018-3a}$$

Dividing by 2018-3a undoes the multiplication by 2018-3a.

$$b=-\frac{2018a}{2018-3a}$$

Variable b cannot be equal to 0.

$$b=-\frac{2018a}{2018-3a}\text{, }b\neq 0$$