Solve x/x-3-3/x^2-9=1

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

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), the least common multiple of x-3,x^{2}-9.

$$\left(x+3\right)x-3=\left(x-3\right)\left(x+3\right)$$

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

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

Consider \left(x-3\right)\left(x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$x^{2}+3x-3=x^{2}-9$$

Subtract x^{2} from both sides.

$$x^{2}+3x-3-x^{2}=-9$$

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

$$3x-3=-9$$

Add 3 to both sides.

$$3x=-9+3$$

Add -9 and 3 to get -6.

$$3x=-6$$

Divide both sides by 3.

$$x=\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$x=-2$$