Solve 144/x+3+144/x-3=66/y+3

$$\frac{ 144 }{ x+3 } + \frac{ 144 }{ x-3 } = \frac{ 66 }{ y+3 }$$

Solve for y (complex solution)

$$y=\frac{11x}{48}-3-\frac{33}{16x}$$

$$x\neq 3\text{ and }x\neq -3\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right)\left(y+3\right), the least common multiple of x+3,x-3,y+3.

$$\left(x-3\right)\left(y+3\right)\times 144+\left(x+3\right)\left(y+3\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply x-3 by y+3.

$$\left(xy+3x-3y-9\right)\times 144+\left(x+3\right)\left(y+3\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply xy+3x-3y-9 by 144.

$$144xy+432x-432y-1296+\left(x+3\right)\left(y+3\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply x+3 by y+3.

$$144xy+432x-432y-1296+\left(xy+3x+3y+9\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply xy+3x+3y+9 by 144.

$$144xy+432x-432y-1296+144xy+432x+432y+1296=\left(x^{2}-9\right)\times 66$$

Combine 144xy and 144xy to get 288xy.

$$288xy+432x-432y-1296+432x+432y+1296=\left(x^{2}-9\right)\times 66$$

Combine 432x and 432x to get 864x.

$$288xy+864x-432y-1296+432y+1296=\left(x^{2}-9\right)\times 66$$

Combine -432y and 432y to get 0.

$$288xy+864x-1296+1296=\left(x^{2}-9\right)\times 66$$

Add -1296 and 1296 to get 0.

$$288xy+864x=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply x^{2}-9 by 66.

$$288xy+864x=66x^{2}-594$$

Subtract 864x from both sides.

$$288xy=66x^{2}-594-864x$$

The equation is in standard form.

$$288xy=66x^{2}-864x-594$$

Divide both sides by 288x.

$$\frac{288xy}{288x}=\frac{66x^{2}-864x-594}{288x}$$

Dividing by 288x undoes the multiplication by 288x.

$$y=\frac{66x^{2}-864x-594}{288x}$$

Divide 66x^{2}-594-864x by 288x.

$$y=\frac{11x}{48}-3-\frac{33}{16x}$$

Variable y cannot be equal to -3.

$$y=\frac{11x}{48}-3-\frac{33}{16x}\text{, }y\neq -3$$

Solve for y

$$y=\frac{11x}{48}-3-\frac{33}{16x}$$

$$x\neq 0\text{ and }|x|\neq 3$$

Steps for Solving Linear Equation

Variable y cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+3\right)\left(y+3\right), the least common multiple of x+3,x-3,y+3.

$$\left(x-3\right)\left(y+3\right)\times 144+\left(x+3\right)\left(y+3\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply x-3 by y+3.

$$\left(xy+3x-3y-9\right)\times 144+\left(x+3\right)\left(y+3\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply xy+3x-3y-9 by 144.

$$144xy+432x-432y-1296+\left(x+3\right)\left(y+3\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply x+3 by y+3.

$$144xy+432x-432y-1296+\left(xy+3x+3y+9\right)\times 144=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply xy+3x+3y+9 by 144.

$$144xy+432x-432y-1296+144xy+432x+432y+1296=\left(x^{2}-9\right)\times 66$$

Combine 144xy and 144xy to get 288xy.

$$288xy+432x-432y-1296+432x+432y+1296=\left(x^{2}-9\right)\times 66$$

Combine 432x and 432x to get 864x.

$$288xy+864x-432y-1296+432y+1296=\left(x^{2}-9\right)\times 66$$

Combine -432y and 432y to get 0.

$$288xy+864x-1296+1296=\left(x^{2}-9\right)\times 66$$

Add -1296 and 1296 to get 0.

$$288xy+864x=\left(x^{2}-9\right)\times 66$$

Use the distributive property to multiply x^{2}-9 by 66.

$$288xy+864x=66x^{2}-594$$

Subtract 864x from both sides.

$$288xy=66x^{2}-594-864x$$

The equation is in standard form.

$$288xy=66x^{2}-864x-594$$

Divide both sides by 288x.

$$\frac{288xy}{288x}=\frac{66x^{2}-864x-594}{288x}$$

Dividing by 288x undoes the multiplication by 288x.

$$y=\frac{66x^{2}-864x-594}{288x}$$

Divide 66x^{2}-594-864x by 288x.

$$y=\frac{11x}{48}-3-\frac{33}{16x}$$

Variable y cannot be equal to -3.

$$y=\frac{11x}{48}-3-\frac{33}{16x}\text{, }y\neq -3$$

Solve for x

$$x=\frac{-3\sqrt{64y^{2}+384y+697}+24y+72}{11}$$

$$x=\frac{3\sqrt{64y^{2}+384y+697}+24y+72}{11}\text{, }y\neq -3$$