Solve 9/6+2/10=a/b

$$\frac { 9 } { 6 } + \frac { 2 } { 10 } = \frac { a } { b }$$

Solve for a

$$a=\frac{17b}{10}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30b, the least common multiple of 6,10,b.

$$5b\times 9+3b\times 2=30a$$

Multiply 5 and 9 to get 45.

$$45b+3b\times 2=30a$$

Multiply 3 and 2 to get 6.

$$45b+6b=30a$$

Combine 45b and 6b to get 51b.

$$51b=30a$$

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

$$30a=51b$$

Divide both sides by 30.

$$\frac{30a}{30}=\frac{51b}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$a=\frac{51b}{30}$$

Divide 51b by 30.

$$a=\frac{17b}{10}$$

Solve for b

$$b=\frac{10a}{17}$$

$$a\neq 0$$

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 30b, the least common multiple of 6,10,b.

$$5b\times 9+3b\times 2=30a$$

Multiply 5 and 9 to get 45.

$$45b+3b\times 2=30a$$

Multiply 3 and 2 to get 6.

$$45b+6b=30a$$

Combine 45b and 6b to get 51b.

$$51b=30a$$

Divide both sides by 51.

$$\frac{51b}{51}=\frac{30a}{51}$$

Dividing by 51 undoes the multiplication by 51.

$$b=\frac{30a}{51}$$

Divide 30a by 51.

$$b=\frac{10a}{17}$$

Variable b cannot be equal to 0.

$$b=\frac{10a}{17}\text{, }b\neq 0$$