Solve x/y+9=x/y-3

$$\frac { x } { y + 9 } = \frac { x } { y } - 3$$

Solve for x

$$x=\frac{y\left(y+9\right)}{3}$$

$$y\neq -9\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y\left(y+9\right), the least common multiple of y+9,y.

$$yx=\left(y+9\right)x+y\left(y+9\right)\left(-3\right)$$

Use the distributive property to multiply y+9 by x.

$$yx=yx+9x+y\left(y+9\right)\left(-3\right)$$

Use the distributive property to multiply y by y+9.

$$yx=yx+9x+\left(y^{2}+9y\right)\left(-3\right)$$

Use the distributive property to multiply y^{2}+9y by -3.

$$yx=yx+9x-3y^{2}-27y$$

Subtract yx from both sides.

$$yx-yx=9x-3y^{2}-27y$$

Combine yx and -yx to get 0.

$$0=9x-3y^{2}-27y$$

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

$$9x-3y^{2}-27y=0$$

Add 3y^{2} to both sides. Anything plus zero gives itself.

$$9x-27y=3y^{2}$$

Add 27y to both sides.

$$9x=3y^{2}+27y$$

Divide both sides by 9.

$$\frac{9x}{9}=\frac{3y\left(y+9\right)}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x=\frac{3y\left(y+9\right)}{9}$$

Divide 3y\left(9+y\right) by 9.

$$x=\frac{y\left(y+9\right)}{3}$$

Solve for y

$$y=\frac{\sqrt{12x+81}-9}{2}$$

$$y=\frac{-\sqrt{12x+81}-9}{2}\text{, }x\neq 0\text{ and }x\geq -\frac{27}{4}$$