Now we can simplify the equation further, but we need to first factor the numerator:
(2(x^2 - 4x - 6))/(x^2 - 9) = (x - 6)/(x - 3)
Now the equation becomes:
2(x^2 - 4x - 6)/(x^2 - 9) = (x - 6)/(x - 3)
At this point, we can cross multiply to solve the equation. After solving the equation, we can verify our solution by substituting it back into the original equation.
To solve this equation, we need to first find a common denominator for all the fractions.
Given expression: 2x - 2/(x + 3) - 18/(x^2 - 9) = (x - 6)/(x - 3)
Rewrite -18/(x^2 - 9) as -18/(x + 3)(x - 3), since x^2 - 9 = (x + 3)(x - 3)
Now, the equation becomes:
2x - 2/(x + 3) - 18/(x + 3)(x - 3) = (x - 6)/(x - 3)
To find a common denominator, we need to multiply the first term by (x - 3)/(x - 3) and the second term by 1:
(2x(x - 3) - 2(x - 3))/(x + 3)(x - 3) - 18/(x + 3)(x - 3) = (x - 6)/(x - 3)
Simplify the expression:
(2x^2 - 6x - 2x + 6 - 18)/(x + 3)(x - 3) = (x - 6)/(x - 3)
Combine like terms:
(2x^2 - 8x - 12)/(x + 3)(x - 3) = (x - 6)/(x - 3)
Now we can simplify the equation further, but we need to first factor the numerator:
(2(x^2 - 4x - 6))/(x^2 - 9) = (x - 6)/(x - 3)
Now the equation becomes:
2(x^2 - 4x - 6)/(x^2 - 9) = (x - 6)/(x - 3)
At this point, we can cross multiply to solve the equation. After solving the equation, we can verify our solution by substituting it back into the original equation.