Solve 1/8h-1/4k=1/2

$$\frac { 1 } { 8 h } - \frac { 1 } { 4 k } = \frac { 1 } { 2 }$$

Solve for h

$$h=\frac{k}{2\left(2k+1\right)}$$

$$k\neq 0\text{ and }k\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Variable h cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8hk, the least common multiple of 8h,4k,2.

$$k-2h=4hk$$

Subtract 4hk from both sides.

$$k-2h-4hk=0$$

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

$$-2h-4hk=-k$$

Combine all terms containing h.

$$\left(-2-4k\right)h=-k$$

The equation is in standard form.

$$\left(-4k-2\right)h=-k$$

Divide both sides by -2-4k.

$$\frac{\left(-4k-2\right)h}{-4k-2}=-\frac{k}{-4k-2}$$

Dividing by -2-4k undoes the multiplication by -2-4k.

$$h=-\frac{k}{-4k-2}$$

Divide -k by -2-4k.

$$h=\frac{k}{2\left(2k+1\right)}$$

Variable h cannot be equal to 0.

$$h=\frac{k}{2\left(2k+1\right)}\text{, }h\neq 0$$

Solve for k

$$k=\frac{2h}{1-4h}$$

$$h\neq 0\text{ and }h\neq \frac{1}{4}$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 8hk, the least common multiple of 8h,4k,2.

$$k-2h=4hk$$

Subtract 4hk from both sides.

$$k-2h-4hk=0$$

Add 2h to both sides. Anything plus zero gives itself.

$$k-4hk=2h$$

Combine all terms containing k.

$$\left(1-4h\right)k=2h$$

Divide both sides by 1-4h.

$$\frac{\left(1-4h\right)k}{1-4h}=\frac{2h}{1-4h}$$

Dividing by 1-4h undoes the multiplication by 1-4h.

$$k=\frac{2h}{1-4h}$$

Variable k cannot be equal to 0.

$$k=\frac{2h}{1-4h}\text{, }k\neq 0$$