Solve f(x)=-3x-4/x-2,e

$$f ( x ) = \frac { - 3 x - 4 } { x - 2 } , e$$

Solve for f

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

$$x\neq 2\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-2.

$$fx\left(x-2\right)=-3x-4$$

Use the distributive property to multiply fx by x-2.

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

Combine all terms containing f.

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

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

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

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

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4f^{2}-28f+9}+2f-3}{2f}\text{; }x=\frac{-\sqrt{4f^{2}-28f+9}+2f-3}{2f}\text{, }&f\neq 0\\x=-\frac{4}{3}\text{, }&f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{4f^{2}-28f+9}+2f-3}{2f}\text{; }x=\frac{-\sqrt{4f^{2}-28f+9}+2f-3}{2f}\text{, }&\left(f\neq 0\text{ and }f\leq \frac{7}{2}-\sqrt{10}\right)\text{ or }f\geq \sqrt{10}+\frac{7}{2}\\x=-\frac{4}{3}\text{, }&f=0\end{matrix}\right.$$