Solve y=1/yx-4

$$y = \frac { 1 } { y } x - 4$$

Solve for x

$$x=y\left(y+4\right)$$

$$y\neq 0$$

Solution Steps

Multiply both sides of the equation by y.

$$yy=1x+y\left(-4\right)$$

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

$$y^{2}=1x+y\left(-4\right)$$

Swap sides so that all variable terms are on the left hand side.

$$1x+y\left(-4\right)=y^{2}$$

Subtract y\left(-4\right) from both sides.

$$1x=y^{2}-y\left(-4\right)$$

Reorder the terms.

$$x=y^{2}-\left(-4y\right)$$

Multiply -1 and -4 to get 4.

$$x=y^{2}+4y$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=-\sqrt{x+4}-2\text{, }&\text{unconditionally}\\y=\sqrt{x+4}-2\text{, }&x\neq 0\end{matrix}\right.$$

Solve for y

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