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.
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.