Solve =f(x)=-x^3+7x^2+12x-20/x^2-4x^2

$$= f ( x ) = \frac { - x ^ { 3 } + 7 x ^ { 2 } + 12 x - 20 } { x ^ { 2 } - 4 x ^ { 2 } }$$

Solve for f

$$f=\frac{1}{3}-\frac{7}{3x}-\frac{4}{x^{2}}+\frac{20}{3x^{3}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -3x^{2}.

$$fx\left(-3\right)x^{2}=-x^{3}+7x^{2}+12x-20$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$fx^{3}\left(-3\right)=-x^{3}+7x^{2}+12x-20$$

The equation is in standard form.

$$\left(-3x^{3}\right)f=-x^{3}+7x^{2}+12x-20$$

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

$$\frac{\left(-3x^{3}\right)f}{-3x^{3}}=\frac{-x^{3}+7x^{2}+12x-20}{-3x^{3}}$$

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

$$f=\frac{-x^{3}+7x^{2}+12x-20}{-3x^{3}}$$

Divide -x^{3}+7x^{2}+12x-20 by -3x^{3}.

$$f=\frac{1}{3}+\frac{-\frac{7x^{2}}{3}-4x+\frac{20}{3}}{x^{3}}$$