Solve 9-x^2/(x-3)(x+3)=-1

$$\frac { 9 - x ^ { 2 } } { ( x - 3 ) ( x + 3 ) } = - 1$$

Solve for x (complex solution)

$$x\in \mathrm{C}\setminus 3,-3$$

Solution Steps

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

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

Use the distributive property to multiply -1 by x-3.

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

Use the distributive property to multiply -x+3 by x+3 and combine like terms.

$$9-x^{2}=-x^{2}+9$$

Add x^{2} to both sides.

$$9-x^{2}+x^{2}=9$$

Combine -x^{2} and x^{2} to get 0.

$$9=9$$

Compare 9 and 9.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Variable x cannot be equal to any of the values -3,3.

$$x\in \mathrm{C}\setminus -3,3$$

Solve for x

$$x\in \mathrm{R}\setminus 3,-3$$

Solution Steps

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

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

Use the distributive property to multiply -1 by x-3.

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

Use the distributive property to multiply -x+3 by x+3 and combine like terms.

$$9-x^{2}=-x^{2}+9$$

Add x^{2} to both sides.

$$9-x^{2}+x^{2}=9$$

Combine -x^{2} and x^{2} to get 0.

$$9=9$$

Compare 9 and 9.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to any of the values -3,3.

$$x\in \mathrm{R}\setminus -3,3$$