Solve 1/a=2-1/bquad[b]

$$\frac { 1 } { a } = 2 - \frac { 1 } { b } \quad [ b ]$$

Solve for a

$$a=1$$

$$b\neq 0$$

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.

$$b=ab\times 2-a\times 1b$$

Combine ab\times 2 and -ab to get ab.

$$b=ab$$

Swap sides so that all variable terms are on the left hand side.

$$ab=b$$

The equation is in standard form.

$$ba=b$$

Divide both sides by b.

$$\frac{ba}{b}=\frac{b}{b}$$

Dividing by b undoes the multiplication by b.

$$a=\frac{b}{b}$$

Divide b by b.

$$a=1$$

Solve for b

$$b\neq 0$$

$$a=1$$

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.

$$b=ab\times 2-a\times 1b$$

Combine ab\times 2 and -ab to get ab.

$$b=ab$$

Subtract ab from both sides.

$$b-ab=0$$

Combine all terms containing b.

$$\left(1-a\right)b=0$$

Divide 0 by 1-a.

$$b=0$$

Variable b cannot be equal to 0.

$$b\in \emptyset$$