Solve 1/6=x-1/a

$$\frac { 1 } { 6 } = x - \frac { 1 } { a }$$

Solve for a

$$a=-\frac{6}{1-6x}$$

$$x\neq \frac{1}{6}$$

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 6a, the least common multiple of 6,a.

$$a=6ax-6$$

Subtract 6ax from both sides.

$$a-6ax=-6$$

Combine all terms containing a.

$$\left(1-6x\right)a=-6$$

Divide both sides by -6x+1.

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

Dividing by -6x+1 undoes the multiplication by -6x+1.

$$a=-\frac{6}{1-6x}$$

Variable a cannot be equal to 0.

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

Solve for x

$$x=\frac{1}{6}+\frac{1}{a}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6a, the least common multiple of 6,a.

$$a=6ax-6$$

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

$$6ax-6=a$$

Add 6 to both sides.

$$6ax=a+6$$

Divide both sides by 6a.

$$\frac{6ax}{6a}=\frac{a+6}{6a}$$

Dividing by 6a undoes the multiplication by 6a.

$$x=\frac{a+6}{6a}$$

Divide a+6 by 6a.

$$x=\frac{1}{6}+\frac{1}{a}$$