Solve a(x^3-x^2)+2/x^3=y

$$\frac{ a( { x }^{ 3 } - { x }^{ 2 } )+2 }{ { x }^{ 3 } } =y$$

Solve for a

$$\left\{\begin{matrix}a=\frac{yx^{3}-2}{\left(x-1\right)x^{2}}\text{, }&x\neq 0\text{ and }x\neq 1\\a\in \mathrm{R}\text{, }&y=2\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a\left(x^{3}-x^{2}\right)+2=yx^{3}$$

Use the distributive property to multiply a by x^{3}-x^{2}.

$$ax^{3}-ax^{2}+2=yx^{3}$$

Subtract 2 from both sides.

$$ax^{3}-ax^{2}=yx^{3}-2$$

Combine all terms containing a.

$$\left(x^{3}-x^{2}\right)a=yx^{3}-2$$

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

$$\frac{\left(x^{3}-x^{2}\right)a}{x^{3}-x^{2}}=\frac{yx^{3}-2}{x^{3}-x^{2}}$$

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

$$a=\frac{yx^{3}-2}{x^{3}-x^{2}}$$

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

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