Solve xy=x+1/x5

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

Solve for y

$$y=\frac{5\left(x+1\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$xyx=\left(x+1\right)\times 5$$

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

$$x^{2}y=\left(x+1\right)\times 5$$

Use the distributive property to multiply x+1 by 5.

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

Divide both sides by x^{2}.

$$\frac{x^{2}y}{x^{2}}=\frac{5x+5}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$y=\frac{5x+5}{x^{2}}$$

Divide 5+5x by x^{2}.

$$y=\frac{5\left(x+1\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{20y+25}+5}{2y}\text{; }x=\frac{-\sqrt{20y+25}+5}{2y}\text{, }&y\neq 0\\x=-1\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{20y+25}+5}{2y}\text{; }x=\frac{-\sqrt{20y+25}+5}{2y}\text{, }&y\neq 0\text{ and }y\geq -\frac{5}{4}\\x=-1\text{, }&y=0\end{matrix}\right.$$