Solve (fg)x=sqrt{x}(x)

$$( f g ) x = \sqrt { x } ( x )$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{\sqrt{x}}{g}\text{, }&g\neq 0\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$gxf=\sqrt{x}x$$

Divide both sides by gx.

$$\frac{gxf}{gx}=\frac{x^{\frac{3}{2}}}{gx}$$

Dividing by gx undoes the multiplication by gx.

$$f=\frac{x^{\frac{3}{2}}}{gx}$$

Divide x^{\frac{3}{2}} by gx.

$$f=\frac{\sqrt{x}}{g}$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{\sqrt{x}}{f}\text{, }&f\neq 0\\g\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$fxg=\sqrt{x}x$$

Divide both sides by fx.

$$\frac{fxg}{fx}=\frac{x^{\frac{3}{2}}}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$g=\frac{x^{\frac{3}{2}}}{fx}$$

Divide x^{\frac{3}{2}} by fx.

$$g=\frac{\sqrt{x}}{f}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{\sqrt{x}}{g}\text{, }&g\neq 0\text{ and }x\geq 0\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$gxf=\sqrt{x}x$$

Divide both sides by gx.

$$\frac{gxf}{gx}=\frac{x^{\frac{3}{2}}}{gx}$$

Dividing by gx undoes the multiplication by gx.

$$f=\frac{x^{\frac{3}{2}}}{gx}$$

Divide x^{\frac{3}{2}} by gx.

$$f=\frac{\sqrt{x}}{g}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{\sqrt{x}}{f}\text{, }&f\neq 0\text{ and }x\geq 0\\g\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$fxg=\sqrt{x}x$$

Divide both sides by fx.

$$\frac{fxg}{fx}=\frac{x^{\frac{3}{2}}}{fx}$$

Dividing by fx undoes the multiplication by fx.

$$g=\frac{x^{\frac{3}{2}}}{fx}$$

Divide x^{\frac{3}{2}} by fx.

$$g=\frac{\sqrt{x}}{f}$$