Solve 1/a+1/b=2

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

Solve for a

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

$$b\neq 0\text{ and }b\neq \frac{1}{2}$$

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 ab, the least common multiple of a,b.

$$b+a=2ab$$

Subtract 2ab from both sides.

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

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

$$a-2ab=-b$$

Combine all terms containing a.

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

Divide both sides by 1-2b.

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

Dividing by 1-2b undoes the multiplication by 1-2b.

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

Variable a cannot be equal to 0.

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

Solve for b

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

$$a\neq 0\text{ and }a\neq \frac{1}{2}$$

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 ab, the least common multiple of a,b.

$$b+a=2ab$$

Subtract 2ab from both sides.

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

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

$$b-2ab=-a$$

Combine all terms containing b.

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

Divide both sides by 1-2a.

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

Dividing by 1-2a undoes the multiplication by 1-2a.

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

Variable b cannot be equal to 0.

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