Solve A/x^2+B/y^2=9

$$\frac { A } { x ^ { 2 } } + \frac { B } { y ^ { 2 } } = 9$$

Solve for A

$$A=-\left(\frac{x}{y}\right)^{2}\left(B-9y^{2}\right)$$

$$x\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

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

$$y^{2}A+x^{2}B=9x^{2}y^{2}$$

Subtract x^{2}B from both sides.

$$y^{2}A=9x^{2}y^{2}-x^{2}B$$

Reorder the terms.

$$Ay^{2}=9x^{2}y^{2}-Bx^{2}$$

The equation is in standard form.

$$y^{2}A=9x^{2}y^{2}-Bx^{2}$$

Divide both sides by y^{2}.

$$\frac{y^{2}A}{y^{2}}=\frac{x^{2}\left(9y^{2}-B\right)}{y^{2}}$$

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

$$A=\frac{x^{2}\left(9y^{2}-B\right)}{y^{2}}$$

Solve for B

$$B=-\left(\frac{y}{x}\right)^{2}\left(A-9x^{2}\right)$$

$$x\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

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

$$y^{2}A+x^{2}B=9x^{2}y^{2}$$

Subtract y^{2}A from both sides.

$$x^{2}B=9x^{2}y^{2}-y^{2}A$$

Reorder the terms.

$$Bx^{2}=9x^{2}y^{2}-Ay^{2}$$

The equation is in standard form.

$$x^{2}B=9x^{2}y^{2}-Ay^{2}$$

Divide both sides by x^{2}.

$$\frac{x^{2}B}{x^{2}}=\frac{y^{2}\left(9x^{2}-A\right)}{x^{2}}$$

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

$$B=\frac{y^{2}\left(9x^{2}-A\right)}{x^{2}}$$