X/x-3-5/x+3 =18/ x^2-9

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To solve for x, we can first find a common denominator for the fractions on the left side of the equation. The common denominator will be (x-3)*(x+3) = x^2 - 9.

Now we rewrite the equation with the common denominator:

(x(x+3) - 5(x-3))/(x-3)(x+3) = 18 / (x^2 - 9)

Expand the terms in the numerator:

(x^2 + 3x - 5x + 15)/(x^2 - 9) = 18 / (x^2 - 9)

Combine like terms:

(x^2 - 2x + 15)/(x^2 - 9) = 18 / (x^2 - 9)

Since the denominators are equal to each other, we can eliminate them:

x^2 - 2x + 15 = 18

Now we have a quadratic equation that we can solve. Rearrange to get all terms on one side:

x^2 - 2x + 15 - 18 = 0
x^2 - 2x - 3 = 0

Factor the quadratic equation or use the quadratic formula:

(x - 3)(x + 1) = 0

This gives us two possible solutions:

x = 3 or x = -1

Therefore, the solutions to the equation are x = 3 or x = -1.