Solve a/2+a/b+a/12+a/2a=1

$$\frac { a } { 2 } + \frac { a } { b } + \frac { a } { 12 } + \frac { a } { 2 a } = 1$$

Solve for b

$$b=-\frac{12a}{7a-6}$$

$$a\neq 0\text{ and }a\neq \frac{6}{7}$$

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 12ab, the least common multiple of 2,b,12,2a.

$$6aba+12aa+aba+6ba=12ab$$

Multiply a and a to get a^{2}.

$$6a^{2}b+12aa+aba+6ba=12ab$$

Multiply a and a to get a^{2}.

$$6a^{2}b+12a^{2}+aba+6ba=12ab$$

Multiply a and a to get a^{2}.

$$6a^{2}b+12a^{2}+a^{2}b+6ba=12ab$$

Combine 6a^{2}b and a^{2}b to get 7a^{2}b.

$$7a^{2}b+12a^{2}+6ba=12ab$$

Subtract 12ab from both sides.

$$7a^{2}b+12a^{2}+6ba-12ab=0$$

Combine 6ba and -12ab to get -6ba.

$$7a^{2}b+12a^{2}-6ba=0$$

Subtract 12a^{2} from both sides. Anything subtracted from zero gives its negation.

$$7a^{2}b-6ba=-12a^{2}$$

Combine all terms containing b.

$$\left(7a^{2}-6a\right)b=-12a^{2}$$

Divide both sides by 7a^{2}-6a.

$$\frac{\left(7a^{2}-6a\right)b}{7a^{2}-6a}=-\frac{12a^{2}}{7a^{2}-6a}$$

Dividing by 7a^{2}-6a undoes the multiplication by 7a^{2}-6a.

$$b=-\frac{12a^{2}}{7a^{2}-6a}$$

Divide -12a^{2} by 7a^{2}-6a.

$$b=-\frac{12a}{7a-6}$$

Variable b cannot be equal to 0.

$$b=-\frac{12a}{7a-6}\text{, }b\neq 0$$

Solve for a

$$a=\frac{6b}{7b+12}$$

$$b\neq -\frac{12}{7}\text{ and }b\neq 0$$