Solve x/a+x/b=2

$$\frac { x } { a } + \frac { x } { b } = 2$$

Solve for a

$$a=-\frac{bx}{x-2b}$$

$$b\neq 0\text{ and }x\neq 0\text{ and }x\neq 2b$$

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 ab, the least common multiple of a,b.

$$bx+ax=2ab$$

Subtract 2ab from both sides.

$$bx+ax-2ab=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ax-2ab=-bx$$

Combine all terms containing a.

$$\left(x-2b\right)a=-bx$$

Divide both sides by x-2b.

$$\frac{\left(x-2b\right)a}{x-2b}=-\frac{bx}{x-2b}$$

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

$$a=-\frac{bx}{x-2b}$$

Variable a cannot be equal to 0.

$$a=-\frac{bx}{x-2b}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{ax}{x-2a}$$

$$a\neq 0\text{ and }x\neq 0\text{ and }x\neq 2a$$

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 ab, the least common multiple of a,b.

$$bx+ax=2ab$$

Subtract 2ab from both sides.

$$bx+ax-2ab=0$$

Subtract ax from both sides. Anything subtracted from zero gives its negation.

$$bx-2ab=-ax$$

Combine all terms containing b.

$$\left(x-2a\right)b=-ax$$

Divide both sides by x-2a.

$$\frac{\left(x-2a\right)b}{x-2a}=-\frac{ax}{x-2a}$$

Dividing by x-2a undoes the multiplication by x-2a.

$$b=-\frac{ax}{x-2a}$$

Variable b cannot be equal to 0.

$$b=-\frac{ax}{x-2a}\text{, }b\neq 0$$