Solve 1/c=3/a+2/b

$$\frac { 1 } { c } = \frac { 3 } { a } + \frac { 2 } { b }$$

Solve for a

$$a=-\frac{3bc}{2c-b}$$

$$b\neq 0\text{ and }c\neq 0\text{ and }c\neq \frac{b}{2}$$

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 abc, the least common multiple of c,a,b.

$$ab=bc\times 3+ac\times 2$$

Subtract ac\times 2 from both sides.

$$ab-ac\times 2=bc\times 3$$

Multiply -1 and 2 to get -2.

$$ab-2ac=bc\times 3$$

Combine all terms containing a.

$$\left(b-2c\right)a=bc\times 3$$

The equation is in standard form.

$$\left(b-2c\right)a=3bc$$

Divide both sides by b-2c.

$$\frac{\left(b-2c\right)a}{b-2c}=\frac{3bc}{b-2c}$$

Dividing by b-2c undoes the multiplication by b-2c.

$$a=\frac{3bc}{b-2c}$$

Variable a cannot be equal to 0.

$$a=\frac{3bc}{b-2c}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{2ac}{3c-a}$$

$$a\neq 0\text{ and }c\neq 0\text{ and }c\neq \frac{a}{3}$$

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 abc, the least common multiple of c,a,b.

$$ab=bc\times 3+ac\times 2$$

Subtract bc\times 3 from both sides.

$$ab-bc\times 3=ac\times 2$$

Multiply -1 and 3 to get -3.

$$ab-3bc=ac\times 2$$

Combine all terms containing b.

$$\left(a-3c\right)b=ac\times 2$$

The equation is in standard form.

$$\left(a-3c\right)b=2ac$$

Divide both sides by a-3c.

$$\frac{\left(a-3c\right)b}{a-3c}=\frac{2ac}{a-3c}$$

Dividing by a-3c undoes the multiplication by a-3c.

$$b=\frac{2ac}{a-3c}$$

Variable b cannot be equal to 0.

$$b=\frac{2ac}{a-3c}\text{, }b\neq 0$$