Solve limx^2-x/x^3=x^2

$$\lim \frac { x ^ { 2 } - x } { x ^ { 3 } } = x ^ { 2 }$$

Solve for l

$$l=\frac{x^{2}}{-Im(\frac{1}{x^{2}})+Re(\frac{1}{x^{2}})Im(x)+Im(\frac{1}{x^{2}})Re(x)}$$

$$Im(\frac{1}{x^{2}})\left(Re(x)-1\right)+Re(\frac{1}{x^{2}})Im(x)\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{x^{2}-x}{x^{3}}.

$$lIm(\frac{x\left(x-1\right)}{x^{3}})=x^{2}$$

Cancel out x in both numerator and denominator.

$$lIm(\frac{x-1}{x^{2}})=x^{2}$$

The equation is in standard form.

$$\left(Im(\frac{1}{x^{2}})\left(Re(x)-1\right)+Re(\frac{1}{x^{2}})Im(x)\right)l=x^{2}$$

Divide both sides by \left(Re(x)-1\right)Im(x^{-2})+Im(x)Re(x^{-2}).

$$\frac{\left(Im(\frac{1}{x^{2}})\left(Re(x)-1\right)+Re(\frac{1}{x^{2}})Im(x)\right)l}{Im(\frac{1}{x^{2}})\left(Re(x)-1\right)+Re(\frac{1}{x^{2}})Im(x)}=\frac{x^{2}}{Im(\frac{1}{x^{2}})\left(Re(x)-1\right)+Re(\frac{1}{x^{2}})Im(x)}$$

Dividing by \left(Re(x)-1\right)Im(x^{-2})+Im(x)Re(x^{-2}) undoes the multiplication by \left(Re(x)-1\right)Im(x^{-2})+Im(x)Re(x^{-2}).

$$l=\frac{x^{2}}{Im(\frac{1}{x^{2}})\left(Re(x)-1\right)+Re(\frac{1}{x^{2}})Im(x)}$$

Divide x^{2} by \left(Re(x)-1\right)Im(x^{-2})+Im(x)Re(x^{-2}).

$$l=\frac{x^{2}}{-Im(\frac{1}{x^{2}})+Re(\frac{1}{x^{2}})Im(x)+Im(\frac{1}{x^{2}})Re(x)}$$