Solve 3/b=d-4/c

$$\frac { 3 } { b } = d - \frac { 4 } { c }$$

Solve for b

$$b=-\frac{3c}{4-cd}$$

$$c\neq 0\text{ and }d\neq \frac{4}{c}$$

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 bc, the least common multiple of b,c.

$$c\times 3=bcd-b\times 4$$

Swap sides so that all variable terms are on the left hand side.

$$bcd-b\times 4=c\times 3$$

Multiply -1 and 4 to get -4.

$$bcd-4b=c\times 3$$

Combine all terms containing b.

$$\left(cd-4\right)b=c\times 3$$

The equation is in standard form.

$$\left(cd-4\right)b=3c$$

Divide both sides by cd-4.

$$\frac{\left(cd-4\right)b}{cd-4}=\frac{3c}{cd-4}$$

Dividing by cd-4 undoes the multiplication by cd-4.

$$b=\frac{3c}{cd-4}$$

Variable b cannot be equal to 0.

$$b=\frac{3c}{cd-4}\text{, }b\neq 0$$

Solve for c

$$c=-\frac{4b}{3-bd}$$

$$b\neq 0\text{ and }\left(d=0\text{ or }b\neq \frac{3}{d}\right)$$

Steps for Solving Linear Equation

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

$$c\times 3=bcd-b\times 4$$

Subtract bcd from both sides.

$$c\times 3-bcd=-b\times 4$$

Multiply -1 and 4 to get -4.

$$c\times 3-bcd=-4b$$

Combine all terms containing c.

$$\left(3-bd\right)c=-4b$$

Divide both sides by 3-bd.

$$\frac{\left(3-bd\right)c}{3-bd}=-\frac{4b}{3-bd}$$

Dividing by 3-bd undoes the multiplication by 3-bd.

$$c=-\frac{4b}{3-bd}$$

Variable c cannot be equal to 0.

$$c=-\frac{4b}{3-bd}\text{, }c\neq 0$$