Solve 87/520=1/a+1/b

$$\frac { 87 } { 520 } = \frac { 1 } { a } + \frac { 1 } { b }$$

Solve for a

$$a=-\frac{520b}{520-87b}$$

$$b\neq 0\text{ and }b\neq \frac{520}{87}$$

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 520ab, the least common multiple of 520,a,b.

$$87ab=520b+520a$$

Subtract 520a from both sides.

$$87ab-520a=520b$$

Combine all terms containing a.

$$\left(87b-520\right)a=520b$$

Divide both sides by 87b-520.

$$\frac{\left(87b-520\right)a}{87b-520}=\frac{520b}{87b-520}$$

Dividing by 87b-520 undoes the multiplication by 87b-520.

$$a=\frac{520b}{87b-520}$$

Variable a cannot be equal to 0.

$$a=\frac{520b}{87b-520}\text{, }a\neq 0$$

Solve for b

$$b=-\frac{520a}{520-87a}$$

$$a\neq 0\text{ and }a\neq \frac{520}{87}$$

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 520ab, the least common multiple of 520,a,b.

$$87ab=520b+520a$$

Subtract 520b from both sides.

$$87ab-520b=520a$$

Combine all terms containing b.

$$\left(87a-520\right)b=520a$$

Divide both sides by 87a-520.

$$\frac{\left(87a-520\right)b}{87a-520}=\frac{520a}{87a-520}$$

Dividing by 87a-520 undoes the multiplication by 87a-520.

$$b=\frac{520a}{87a-520}$$

Variable b cannot be equal to 0.

$$b=\frac{520a}{87a-520}\text{, }b\neq 0$$