Solve 1000/h+2000/x=1000

$$\frac { 1000 } { h } + \frac { 2000 } { x } = 1000$$

Solve for h

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

$$x\neq 0\text{ and }x\neq 2$$

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 hx, the least common multiple of h,x.

$$x\times 1000+h\times 2000=1000hx$$

Subtract 1000hx from both sides.

$$x\times 1000+h\times 2000-1000hx=0$$

Subtract x\times 1000 from both sides. Anything subtracted from zero gives its negation.

$$h\times 2000-1000hx=-x\times 1000$$

Multiply -1 and 1000 to get -1000.

$$h\times 2000-1000hx=-1000x$$

Combine all terms containing h.

$$\left(2000-1000x\right)h=-1000x$$

Divide both sides by 2000-1000x.

$$\frac{\left(2000-1000x\right)h}{2000-1000x}=-\frac{1000x}{2000-1000x}$$

Dividing by 2000-1000x undoes the multiplication by 2000-1000x.

$$h=-\frac{1000x}{2000-1000x}$$

Divide -1000x by 2000-1000x.

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

Variable h cannot be equal to 0.

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

Solve for x

$$x=-\frac{2h}{1-h}$$

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

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 hx, the least common multiple of h,x.

$$x\times 1000+h\times 2000=1000hx$$

Subtract 1000hx from both sides.

$$x\times 1000+h\times 2000-1000hx=0$$

Subtract h\times 2000 from both sides. Anything subtracted from zero gives its negation.

$$x\times 1000-1000hx=-h\times 2000$$

Multiply -1 and 2000 to get -2000.

$$x\times 1000-1000hx=-2000h$$

Combine all terms containing x.

$$\left(1000-1000h\right)x=-2000h$$

Divide both sides by 1000-1000h.

$$\frac{\left(1000-1000h\right)x}{1000-1000h}=-\frac{2000h}{1000-1000h}$$

Dividing by 1000-1000h undoes the multiplication by 1000-1000h.

$$x=-\frac{2000h}{1000-1000h}$$

Divide -2000h by 1000-1000h.

$$x=-\frac{2h}{1-h}$$

Variable x cannot be equal to 0.

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