Solve 5/x+5/y=1/xy

$$\frac { 5 } { x } + \frac { 5 } { y } = 1 / x y$$

Solve for x

$$x=\frac{y\left(y-5\right)}{5}$$

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

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 xy, the least common multiple of x,y.

$$y\times 5+x\times 5=y\times 1y$$

Multiply y and y to get y^{2}.

$$y\times 5+x\times 5=y^{2}\times 1$$

Subtract y\times 5 from both sides.

$$x\times 5=y^{2}\times 1-y\times 5$$

Reorder the terms.

$$5x=y^{2}-5y$$

Divide both sides by 5.

$$\frac{5x}{5}=\frac{y\left(y-5\right)}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=\frac{y\left(y-5\right)}{5}$$

Variable x cannot be equal to 0.

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

Solve for y (complex solution)

$$y=\frac{-\sqrt{20x+25}+5}{2}$$

$$y=\frac{\sqrt{20x+25}+5}{2}\text{, }x\neq 0$$

Solve for y

$$y=\frac{-\sqrt{20x+25}+5}{2}$$

$$y=\frac{\sqrt{20x+25}+5}{2}\text{, }x\geq -\frac{5}{4}\text{ and }x\neq 0$$