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

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

Solve for A

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by xy^{2}, the least common multiple of x^{1},y^{2}.

$$y^{2}A+xB=9xy^{2}$$

Subtract xB from both sides.

$$y^{2}A=9xy^{2}-xB$$

The equation is in standard form.

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

Divide both sides by y^{2}.

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

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

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

Divide x\left(9y^{2}-B\right) by y^{2}.

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

Solve for B

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by xy^{2}, the least common multiple of x^{1},y^{2}.

$$y^{2}A+xB=9xy^{2}$$

Subtract y^{2}A from both sides.

$$xB=9xy^{2}-y^{2}A$$

Reorder the terms.

$$Bx=9xy^{2}-Ay^{2}$$

The equation is in standard form.

$$xB=9xy^{2}-Ay^{2}$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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