Solve 200/a+200/b=40

$$\frac { 200 } { a } + \frac { 200 } { b } = 40$$

Solve for a

$$a=-\frac{5b}{5-b}$$

$$b\neq 0\text{ and }b\neq 5$$

Steps for Solving Linear Equation

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

$$b\times 200+a\times 200=40ab$$

Subtract 40ab from both sides.

$$b\times 200+a\times 200-40ab=0$$

Subtract b\times 200 from both sides. Anything subtracted from zero gives its negation.

$$a\times 200-40ab=-b\times 200$$

Multiply -1 and 200 to get -200.

$$a\times 200-40ab=-200b$$

Combine all terms containing a.

$$\left(200-40b\right)a=-200b$$

Divide both sides by 200-40b.

$$\frac{\left(200-40b\right)a}{200-40b}=-\frac{200b}{200-40b}$$

Dividing by 200-40b undoes the multiplication by 200-40b.

$$a=-\frac{200b}{200-40b}$$

Divide -200b by 200-40b.

$$a=-\frac{5b}{5-b}$$

Variable a cannot be equal to 0.

$$a=-\frac{5b}{5-b}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{5a}{5-a}$$

$$a\neq 0\text{ and }a\neq 5$$

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 ab, the least common multiple of a,b.

$$b\times 200+a\times 200=40ab$$

Subtract 40ab from both sides.

$$b\times 200+a\times 200-40ab=0$$

Subtract a\times 200 from both sides. Anything subtracted from zero gives its negation.

$$b\times 200-40ab=-a\times 200$$

Multiply -1 and 200 to get -200.

$$b\times 200-40ab=-200a$$

Combine all terms containing b.

$$\left(200-40a\right)b=-200a$$

Divide both sides by 200-40a.

$$\frac{\left(200-40a\right)b}{200-40a}=-\frac{200a}{200-40a}$$

Dividing by 200-40a undoes the multiplication by 200-40a.

$$b=-\frac{200a}{200-40a}$$

Divide -200a by 200-40a.

$$b=-\frac{5a}{5-a}$$

Variable b cannot be equal to 0.

$$b=-\frac{5a}{5-a}\text{, }b\neq 0$$