Solve Fx=3x+1/x+2

$$Fx = \frac{ 3x+1 }{ x+2 }$$

Solve for F

$$F=\frac{3x+1}{x\left(x+2\right)}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by x+2.

$$Fx\left(x+2\right)=3x+1$$

Use the distributive property to multiply Fx by x+2.

$$Fx^{2}+2Fx=3x+1$$

Combine all terms containing F.

$$\left(x^{2}+2x\right)F=3x+1$$

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

$$\frac{\left(x^{2}+2x\right)F}{x^{2}+2x}=\frac{3x+1}{x^{2}+2x}$$

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

$$F=\frac{3x+1}{x^{2}+2x}$$

Divide 3x+1 by x^{2}+2x.

$$F=\frac{3x+1}{x\left(x+2\right)}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{4F^{2}-8F+9}-2F+3}{2F}\text{; }x=\frac{-\sqrt{4F^{2}-8F+9}-2F+3}{2F}\text{, }&F\neq 0\\x=-\frac{1}{3}\text{, }&F=0\end{matrix}\right.$$