Rational equation

-5/x-3 - 3/x+3=2/x^2-9
how do I solve?

multiply everything by x^2-9, which gives you:

-5(x+3)-3(x-3)=2
Have fun!

9(x+3)-3(x+3)=2

9x+27+3-9=2
6x-36
6x=48
x=8

Is this right?

I apologize! I misread your equation. Multiply through by x^2 gives:

9x^2-8x-2=0. Use Quadratic Formula to get two solutions: (8+sqrt(136))/18 and (8-sqrt(136))/18. I checked, and both work!

To solve the rational equation (-5/(x-3)) - (3/(x+3)) = 2/(x^2-9), follow these steps:

Step 1: Simplify the equation:

First, let's simplify all the terms in the equation:
-5/(x-3) - 3/(x+3) = 2/(x^2-9)

To combine the fractions, we need to find a common denominator. In this case, the common denominator is (x-3)(x+3), which is the product of the denominators of both fractions.

Multiply each term by the necessary factors to get a common denominator:

(-5(x+3))/((x-3)(x+3)) - (3(x-3))/((x+3)(x-3)) = (2)/((x+3)(x-3))

Simplifying further, you would end up with:

(-5x - 15 - 3x + 9)/((x-3)(x+3)) = 2/((x+3)(x-3))

Combining like terms:

(-8x - 6)/((x-3)(x+3)) = 2/((x+3)(x-3))

Step 2: Eliminate the denominators:

To eliminate the denominators, you can multiply each side of the equation by (x-3)(x+3). This ensures that the denominators cancel out:

[(x-3)(x+3)] * [(-8x - 6)/((x-3)(x+3))] = [(x-3)(x+3)] * [2/((x+3)(x-3))]

Simplifying further:

(-8x - 6) = 2

Step 3: Solve for x:

Next, solve the resulting equation from step 2 for x:

-8x - 6 = 2

Add 6 to both sides:

-8x = 8

Divide both sides by -8:

x = -1

Therefore, the solution to the rational equation is x = -1.

Note: Before finalizing the solution, make sure to check if the obtained value satisfies any excluded values, in this case x=±3.