Solve e=1-frac{Q_{c}}{Q_{h}}

$$e = 1 - \frac { Q _ { c } } { Q _ { h } }$$

Solve for Q_c

$$Q_{c}=\left(1-e\right)Q_{h}$$

$$Q_{h}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by Q_{h}.

$$eQ_{h}=Q_{h}-Q_{c}$$

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

$$Q_{h}-Q_{c}=eQ_{h}$$

Subtract Q_{h} from both sides.

$$-Q_{c}=eQ_{h}-Q_{h}$$

Divide both sides by -1.

$$\frac{-Q_{c}}{-1}=\frac{\left(e-1\right)Q_{h}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$Q_{c}=\frac{\left(e-1\right)Q_{h}}{-1}$$

Divide Q_{h}\left(e-1\right) by -1.

$$Q_{c}=Q_{h}-eQ_{h}$$

Solve for Q_h

$$Q_{h}=-\frac{Q_{c}}{e-1}$$

$$Q_{c}\neq 0$$

Steps for Solving Linear Equation

Variable Q_{h} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by Q_{h}.

$$eQ_{h}=Q_{h}-Q_{c}$$

Subtract Q_{h} from both sides.

$$eQ_{h}-Q_{h}=-Q_{c}$$

Combine all terms containing Q_{h}.

$$\left(e-1\right)Q_{h}=-Q_{c}$$

Divide both sides by e-1.

$$\frac{\left(e-1\right)Q_{h}}{e-1}=-\frac{Q_{c}}{e-1}$$

Dividing by e-1 undoes the multiplication by e-1.

$$Q_{h}=-\frac{Q_{c}}{e-1}$$

Variable Q_{h} cannot be equal to 0.

$$Q_{h}=-\frac{Q_{c}}{e-1}\text{, }Q_{h}\neq 0$$