Solve a-b/b=c-d/d

$$\frac { a - b } { b } = \frac { c - d } { d }$$

Solve for a

$$a=\frac{bc}{d}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by bd, the least common multiple of b,d.

$$d\left(a-b\right)=b\left(c-d\right)$$

Use the distributive property to multiply d by a-b.

$$da-db=b\left(c-d\right)$$

Use the distributive property to multiply b by c-d.

$$da-db=bc-bd$$

Add db to both sides.

$$da=bc-bd+db$$

Combine -bd and db to get 0.

$$da=bc$$

Divide both sides by d.

$$\frac{da}{d}=\frac{bc}{d}$$

Dividing by d undoes the multiplication by d.

$$a=\frac{bc}{d}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{ad}{c}\text{, }&a\neq 0\text{ and }d\neq 0\text{ and }c\neq 0\\b\neq 0\text{, }&a=0\text{ and }c=0\text{ and }d\neq 0\end{matrix}\right.$$

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 bd, the least common multiple of b,d.

$$d\left(a-b\right)=b\left(c-d\right)$$

Use the distributive property to multiply d by a-b.

$$da-db=b\left(c-d\right)$$

Use the distributive property to multiply b by c-d.

$$da-db=bc-bd$$

Subtract bc from both sides.

$$da-db-bc=-bd$$

Add bd to both sides.

$$da-db-bc+bd=0$$

Combine -db and bd to get 0.

$$da-bc=0$$

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

$$-bc=-da$$

Cancel out -1 on both sides.

$$bc=da$$

The equation is in standard form.

$$cb=ad$$

Divide both sides by c.

$$\frac{cb}{c}=\frac{ad}{c}$$

Dividing by c undoes the multiplication by c.

$$b=\frac{ad}{c}$$

Variable b cannot be equal to 0.

$$b=\frac{ad}{c}\text{, }b\neq 0$$