Solve y=A+B/x+C/x^2

$$y = A + \frac { B } { x } + \frac { C } { x ^ { 2 } }$$

Solve for A

$$A=y-\frac{B}{x}-\frac{C}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x,x^{2}.

$$yx^{2}=x^{2}A+xB+C$$

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

$$x^{2}A+xB+C=yx^{2}$$

Subtract xB from both sides.

$$x^{2}A+C=yx^{2}-xB$$

Subtract C from both sides.

$$x^{2}A=yx^{2}-xB-C$$

The equation is in standard form.

$$x^{2}A=yx^{2}-Bx-C$$

Divide both sides by x^{2}.

$$\frac{x^{2}A}{x^{2}}=\frac{yx^{2}-Bx-C}{x^{2}}$$

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

$$A=\frac{yx^{2}-Bx-C}{x^{2}}$$

Divide yx^{2}-xB-C by x^{2}.

$$A=-\frac{Bx+C}{x^{2}}+y$$

Solve for B

$$B=xy-Ax-\frac{C}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x^{2}, the least common multiple of x,x^{2}.

$$yx^{2}=x^{2}A+xB+C$$

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

$$x^{2}A+xB+C=yx^{2}$$

Subtract x^{2}A from both sides.

$$xB+C=yx^{2}-x^{2}A$$

Subtract C from both sides.

$$xB=yx^{2}-x^{2}A-C$$

Reorder the terms.

$$Bx=-Ax^{2}+yx^{2}-C$$

The equation is in standard form.

$$xB=yx^{2}-Ax^{2}-C$$

Divide both sides by x.

$$\frac{xB}{x}=\frac{yx^{2}-Ax^{2}-C}{x}$$

Dividing by x undoes the multiplication by x.

$$B=\frac{yx^{2}-Ax^{2}-C}{x}$$

Divide -Ax^{2}+yx^{2}-C by x.

$$B=xy-Ax-\frac{C}{x}$$