Solve x-3/x+3-1=-2/x-3

$$\frac{ x-3 }{ x+3 } -1=- \frac{ 2 }{ x-3 }$$

Solve for x

$$x=6$$

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-3.

$$\left(x-3\right)\left(x-3\right)+\left(x-3\right)\left(x+3\right)\left(-1\right)=-\left(x+3\right)\times 2$$

Multiply x-3 and x-3 to get \left(x-3\right)^{2}.

$$\left(x-3\right)^{2}+\left(x-3\right)\left(x+3\right)\left(-1\right)=-\left(x+3\right)\times 2$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$x^{2}-6x+9+\left(x-3\right)\left(x+3\right)\left(-1\right)=-\left(x+3\right)\times 2$$

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

$$x^{2}-6x+9+\left(x^{2}-9\right)\left(-1\right)=-\left(x+3\right)\times 2$$

Use the distributive property to multiply x^{2}-9 by -1.

$$x^{2}-6x+9-x^{2}+9=-\left(x+3\right)\times 2$$

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

$$-6x+9+9=-\left(x+3\right)\times 2$$

Add 9 and 9 to get 18.

$$-6x+18=-\left(x+3\right)\times 2$$

Use the distributive property to multiply x+3 by 2.

$$-6x+18=-\left(2x+6\right)$$

To find the opposite of 2x+6, find the opposite of each term.

$$-6x+18=-2x-6$$

Add 2x to both sides.

$$-6x+18+2x=-6$$

Combine -6x and 2x to get -4x.

$$-4x+18=-6$$

Subtract 18 from both sides.

$$-4x=-6-18$$

Subtract 18 from -6 to get -24.

$$-4x=-24$$

Divide both sides by -4.

$$x=\frac{-24}{-4}$$

Divide -24 by -4 to get 6.

$$x=6$$