Solve 1/a+1/2b=3

$$\frac { 1 } { a } + \frac { 1 } { 2 b } = 3$$

Solve for a

$$a=-\frac{2b}{1-6b}$$

$$b\neq 0\text{ and }b\neq \frac{1}{6}$$

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 2ab, the least common multiple of a,2b.

$$2b+a=6ab$$

Subtract 6ab from both sides.

$$2b+a-6ab=0$$

Subtract 2b from both sides. Anything subtracted from zero gives its negation.

$$a-6ab=-2b$$

Combine all terms containing a.

$$\left(1-6b\right)a=-2b$$

Divide both sides by 1-6b.

$$\frac{\left(1-6b\right)a}{1-6b}=-\frac{2b}{1-6b}$$

Dividing by 1-6b undoes the multiplication by 1-6b.

$$a=-\frac{2b}{1-6b}$$

Variable a cannot be equal to 0.

$$a=-\frac{2b}{1-6b}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{a}{2\left(1-3a\right)}$$

$$a\neq 0\text{ and }a\neq \frac{1}{3}$$

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 2ab, the least common multiple of a,2b.

$$2b+a=6ab$$

Subtract 6ab from both sides.

$$2b+a-6ab=0$$

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

$$2b-6ab=-a$$

Combine all terms containing b.

$$\left(2-6a\right)b=-a$$

Divide both sides by 2-6a.

$$\frac{\left(2-6a\right)b}{2-6a}=-\frac{a}{2-6a}$$

Dividing by 2-6a undoes the multiplication by 2-6a.

$$b=-\frac{a}{2-6a}$$

Divide -a by 2-6a.

$$b=-\frac{a}{2\left(1-3a\right)}$$

Variable b cannot be equal to 0.

$$b=-\frac{a}{2\left(1-3a\right)}\text{, }b\neq 0$$