Solve a+b/2a-3b=3b-a/6a

$$\frac { a + b } { 2 a } - 3 b = \frac { 3 b - a } { 6 a }$$

Solve for a

$$a\neq 0$$

$$b=\frac{2}{9}\text{ and }a\neq 0$$

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 6a, the least common multiple of 2a,6a.

$$3\left(a+b\right)-3b\times 6a=3b-a$$

Use the distributive property to multiply 3 by a+b.

$$3a+3b-3b\times 6a=3b-a$$

Multiply -3 and 6 to get -18.

$$3a+3b-18ba=3b-a$$

Add a to both sides.

$$3a+3b-18ba+a=3b$$

Combine 3a and a to get 4a.

$$4a+3b-18ba=3b$$

Subtract 3b from both sides.

$$4a-18ba=3b-3b$$

Combine 3b and -3b to get 0.

$$4a-18ba=0$$

Combine all terms containing a.

$$\left(4-18b\right)a=0$$

Divide 0 by 4-18b.

$$a=0$$

Variable a cannot be equal to 0.

$$a\in \emptyset$$

Solve for b

$$b = \frac{2}{9} = 0.2222222222222222$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6a, the least common multiple of 2a,6a.

$$3\left(a+b\right)-3b\times 6a=3b-a$$

Use the distributive property to multiply 3 by a+b.

$$3a+3b-3b\times 6a=3b-a$$

Multiply -3 and 6 to get -18.

$$3a+3b-18ba=3b-a$$

Subtract 3b from both sides.

$$3a+3b-18ba-3b=-a$$

Combine 3b and -3b to get 0.

$$3a-18ba=-a$$

Subtract 3a from both sides.

$$-18ba=-a-3a$$

Combine -a and -3a to get -4a.

$$-18ba=-4a$$

The equation is in standard form.

$$\left(-18a\right)b=-4a$$

Divide both sides by -18a.

$$\frac{\left(-18a\right)b}{-18a}=-\frac{4a}{-18a}$$

Dividing by -18a undoes the multiplication by -18a.

$$b=-\frac{4a}{-18a}$$

Divide -4a by -18a.

$$b=\frac{2}{9}$$