Solve x/b-x/a=1

$$\frac { x } { b } - \frac { x } { a } = 1$$

Solve for a

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

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

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 b,a.

$$ax-bx=ab$$

Subtract ab from both sides.

$$ax-bx-ab=0$$

Add bx to both sides. Anything plus zero gives itself.

$$ax-ab=bx$$

Combine all terms containing a.

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

Divide both sides by x-b.

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

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

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

Variable a cannot be equal to 0.

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

Solve for b

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

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

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 b,a.

$$ax-bx=ab$$

Subtract ab from both sides.

$$ax-bx-ab=0$$

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

$$-bx-ab=-ax$$

Combine all terms containing b.

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

Divide both sides by -x-a.

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

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

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

Divide -ax by -x-a.

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

Variable b cannot be equal to 0.

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