Solve x+1/y=1/xx

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

Solve for y

$$y=-\frac{1}{x-1}$$

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

Steps for Solving Linear Equation

Variable y 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 y,x.

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

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

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

Subtract y\times 1x from both sides.

$$x^{2}y+x-y\times 1x=0$$

Reorder the terms.

$$x+yx^{2}-xy=0$$

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

$$yx^{2}-xy=-x$$

Combine all terms containing y.

$$\left(x^{2}-x\right)y=-x$$

Divide both sides by x^{2}-x.

$$\frac{\left(x^{2}-x\right)y}{x^{2}-x}=-\frac{x}{x^{2}-x}$$

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

$$y=-\frac{x}{x^{2}-x}$$

Divide -x by x^{2}-x.

$$y=-\frac{1}{x-1}$$

Variable y cannot be equal to 0.

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

Solve for x

$$x=\frac{y-1}{y}$$

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