Solve 1/f(x)=3x^2-4x

$$1 / f ( x ) = 3 x ^ { 2 } - 4 x$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{1}{4-3x}\text{, }&x\neq \frac{4}{3}\\f\neq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by f.

$$1x=3x^{2}f-4xf$$

Swap sides so that all variable terms are on the left hand side.

$$3x^{2}f-4xf=1x$$

Reorder the terms.

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

Combine all terms containing f.

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

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

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

Dividing by 3x^{2}-4x undoes the multiplication by 3x^{2}-4x.

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

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

$$f=\frac{1}{3x-4}$$

Variable f cannot be equal to 0.

$$f=\frac{1}{3x-4}\text{, }f\neq 0$$

Solve for x

$$x=\frac{4}{3}+\frac{1}{3f}$$

$$x=0\text{, }f\neq 0$$