Solve 3f(x)=2/x+3

$$3 f ( x ) = \frac { 2 } { x + 3 }$$

Solve for f

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

$$x\neq -3\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

$$3fx\left(x+3\right)=2$$

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

$$3fx^{2}+9fx=2$$

Combine all terms containing f.

$$\left(3x^{2}+9x\right)f=2$$

Divide both sides by 3x^{2}+9x.

$$\frac{\left(3x^{2}+9x\right)f}{3x^{2}+9x}=\frac{2}{3x^{2}+9x}$$

Dividing by 3x^{2}+9x undoes the multiplication by 3x^{2}+9x.

$$f=\frac{2}{3x^{2}+9x}$$

Divide 2 by 3x^{2}+9x.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{81f^{2}+24f}}{6f}-\frac{3}{2}$$

$$x=-\frac{\sqrt{81f^{2}+24f}}{6f}-\frac{3}{2}\text{, }f\neq 0$$

Solve for x

$$x=\frac{\sqrt{81f^{2}+24f}}{6f}-\frac{3}{2}$$

$$x=-\frac{\sqrt{81f^{2}+24f}}{6f}-\frac{3}{2}\text{, }f>0\text{ or }f\leq -\frac{8}{27}$$