Solve f(x)=4x/x+3,g

$$f ( x ) = \frac { 4 x } { x + 3 } , g$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{4}{x+3}\text{, }&x\neq -3\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

$$fx\left(x+3\right)=4x$$

Use the distributive property to multiply fx by x+3.

$$fx^{2}+3fx=4x$$

Combine all terms containing f.

$$\left(x^{2}+3x\right)f=4x$$

Divide both sides by x^{2}+3x.

$$\frac{\left(x^{2}+3x\right)f}{x^{2}+3x}=\frac{4x}{x^{2}+3x}$$

Dividing by x^{2}+3x undoes the multiplication by x^{2}+3x.

$$f=\frac{4x}{x^{2}+3x}$$

Divide 4x by x^{2}+3x.

$$f=\frac{4}{x+3}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{4}{x+3}\text{, }&x\neq -3\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

$$fx\left(x+3\right)=4x$$

Use the distributive property to multiply fx by x+3.

$$fx^{2}+3fx=4x$$

Combine all terms containing f.

$$\left(x^{2}+3x\right)f=4x$$

Divide both sides by x^{2}+3x.

$$\frac{\left(x^{2}+3x\right)f}{x^{2}+3x}=\frac{4x}{x^{2}+3x}$$

Dividing by x^{2}+3x undoes the multiplication by x^{2}+3x.

$$f=\frac{4x}{x^{2}+3x}$$

Divide 4x by x^{2}+3x.

$$f=\frac{4}{x+3}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-3+\frac{4}{f}\text{, }&f\neq 0\end{matrix}\right.$$