Solve 1/60h+1/x=1/24

$$\frac { 1 } { 60 h } + \frac { 1 } { x } = \frac { 1 } { 24 }$$

Solve for h

$$h=-\frac{2x}{5\left(24-x\right)}$$

$$x\neq 0\text{ and }x\neq 24$$

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 120hx, the least common multiple of 60h,x,24.

$$2x+120h=5hx$$

Subtract 5hx from both sides.

$$2x+120h-5hx=0$$

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$120h-5hx=-2x$$

Combine all terms containing h.

$$\left(120-5x\right)h=-2x$$

Divide both sides by -5x+120.

$$\frac{\left(120-5x\right)h}{120-5x}=-\frac{2x}{120-5x}$$

Dividing by -5x+120 undoes the multiplication by -5x+120.

$$h=-\frac{2x}{120-5x}$$

Divide -2x by -5x+120.

$$h=-\frac{2x}{5\left(24-x\right)}$$

Variable h cannot be equal to 0.

$$h=-\frac{2x}{5\left(24-x\right)}\text{, }h\neq 0$$

Solve for x

$$x=-\frac{120h}{2-5h}$$

$$h\neq 0\text{ and }h\neq \frac{2}{5}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 120hx, the least common multiple of 60h,x,24.

$$2x+120h=5hx$$

Subtract 5hx from both sides.

$$2x+120h-5hx=0$$

Subtract 120h from both sides. Anything subtracted from zero gives its negation.

$$2x-5hx=-120h$$

Combine all terms containing x.

$$\left(2-5h\right)x=-120h$$

Divide both sides by 2-5h.

$$\frac{\left(2-5h\right)x}{2-5h}=-\frac{120h}{2-5h}$$

Dividing by 2-5h undoes the multiplication by 2-5h.

$$x=-\frac{120h}{2-5h}$$

Variable x cannot be equal to 0.

$$x=-\frac{120h}{2-5h}\text{, }x\neq 0$$