Solve 2/alpha+2/beta=3

$$\frac { 2 } { \alpha } + \frac { 2 } { \beta } = 3$$

Solve for α

$$\alpha =-\frac{2\beta }{2-3\beta }$$

$$\beta \neq 0\text{ and }\beta \neq \frac{2}{3}$$

Steps for Solving Linear Equation

Variable \alpha cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by \alpha \beta , the least common multiple of \alpha ,\beta .

$$\beta \times 2+\alpha \times 2=3\alpha \beta$$

Subtract 3\alpha \beta from both sides.

$$\beta \times 2+\alpha \times 2-3\alpha \beta =0$$

Subtract \beta \times 2 from both sides. Anything subtracted from zero gives its negation.

$$\alpha \times 2-3\alpha \beta =-\beta \times 2$$

Multiply -1 and 2 to get -2.

$$\alpha \times 2-3\alpha \beta =-2\beta$$

Combine all terms containing \alpha .

$$\left(2-3\beta \right)\alpha =-2\beta$$

Divide both sides by 2-3\beta .

$$\frac{\left(2-3\beta \right)\alpha }{2-3\beta }=-\frac{2\beta }{2-3\beta }$$

Dividing by 2-3\beta undoes the multiplication by 2-3\beta .

$$\alpha =-\frac{2\beta }{2-3\beta }$$

Variable \alpha cannot be equal to 0.

$$\alpha =-\frac{2\beta }{2-3\beta }\text{, }\alpha \neq 0$$

Solve for β

$$\beta =-\frac{2\alpha }{2-3\alpha }$$

$$\alpha \neq 0\text{ and }\alpha \neq \frac{2}{3}$$

Steps for Solving Linear Equation

Variable \beta cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by \alpha \beta , the least common multiple of \alpha ,\beta .

$$\beta \times 2+\alpha \times 2=3\alpha \beta$$

Subtract 3\alpha \beta from both sides.

$$\beta \times 2+\alpha \times 2-3\alpha \beta =0$$

Subtract \alpha \times 2 from both sides. Anything subtracted from zero gives its negation.

$$\beta \times 2-3\alpha \beta =-\alpha \times 2$$

Multiply -1 and 2 to get -2.

$$\beta \times 2-3\alpha \beta =-2\alpha$$

Combine all terms containing \beta .

$$\left(2-3\alpha \right)\beta =-2\alpha$$

Divide both sides by 2-3\alpha .

$$\frac{\left(2-3\alpha \right)\beta }{2-3\alpha }=-\frac{2\alpha }{2-3\alpha }$$

Dividing by 2-3\alpha undoes the multiplication by 2-3\alpha .

$$\beta =-\frac{2\alpha }{2-3\alpha }$$

Variable \beta cannot be equal to 0.

$$\beta =-\frac{2\alpha }{2-3\alpha }\text{, }\beta \neq 0$$