Solve y=sqrt{3-x}operatorname{tarctan}1/x

$$y = \sqrt { 3 - x } \operatorname { tarctan } \frac { 1 } { x }$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=\frac{\left(3-x\right)^{-\frac{1}{2}}y}{\arctan(\frac{1}{x})}\text{, }&x\neq 3\text{ and }x\neq 0\\t\in \mathrm{C}\text{, }&x=3\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\sqrt{3-x}t\arctan(\frac{1}{x})=y$$

The equation is in standard form.

$$\sqrt{3-x}\arctan(\frac{1}{x})t=y$$

Divide both sides by \sqrt{3-x}\arctan(x^{-1}).

$$\frac{\sqrt{3-x}\arctan(\frac{1}{x})t}{\sqrt{3-x}\arctan(\frac{1}{x})}=\frac{y}{\sqrt{3-x}\arctan(\frac{1}{x})}$$

Dividing by \sqrt{3-x}\arctan(x^{-1}) undoes the multiplication by \sqrt{3-x}\arctan(x^{-1}).

$$t=\frac{y}{\sqrt{3-x}\arctan(\frac{1}{x})}$$

Divide y by \sqrt{3-x}\arctan(x^{-1}).

$$t=\frac{\left(3-x\right)^{-\frac{1}{2}}y}{\arctan(\frac{1}{x})}$$

Solve for t

$$\left\{\begin{matrix}t=\frac{y}{\sqrt{3-x}\arctan(\frac{1}{x})}\text{, }&x\neq 0\text{ and }x<3\\t\in \mathrm{R}\text{, }&y=0\text{ and }x=3\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\sqrt{3-x}t\arctan(\frac{1}{x})=y$$

The equation is in standard form.

$$\sqrt{3-x}\arctan(\frac{1}{x})t=y$$

Divide both sides by \sqrt{3-x}\arctan(x^{-1}).

$$\frac{\sqrt{3-x}\arctan(\frac{1}{x})t}{\sqrt{3-x}\arctan(\frac{1}{x})}=\frac{y}{\sqrt{3-x}\arctan(\frac{1}{x})}$$

Dividing by \sqrt{3-x}\arctan(x^{-1}) undoes the multiplication by \sqrt{3-x}\arctan(x^{-1}).

$$t=\frac{y}{\sqrt{3-x}\arctan(\frac{1}{x})}$$