To solve this equation, we first need to find a common denominator for all fractions on both sides.
Multiplying the first fraction by (x-2)/(x-2), the second fraction by (x+2)/(x+2), and the third fraction by x(x+2)/(x(x+2), we get:
(18(x-2))/(x(x-2)) + (14(x+2))/(x(x+2)) = 20/(x-2)
Expanding the fractions, we get:
(18x - 36)/(x^2 - 2x) + (14x + 28)/(x^2 + 2x) = 20/(x-2)
Combining the fractions, we get:
(32x - 8)/(x^2 - 4) = 20/(x-2)
Cross multiplying, we get:
20(x^2 - 4) = 32x - 8(x-2)20x^2 - 80 = 32x - 8x + 1620x^2 - 24x - 64 = 0
Dividing through by 4, we get:
5x^2 - 6x - 16 = 0
Solving this quadratic equation, we find two possible solutions:
x = 2 or x = -1.6
But, we need to check if these are valid solutions by plugging back into the original equation. After checking, we find that x = 2 is a valid solution.
To solve this equation, we first need to find a common denominator for all fractions on both sides.
Multiplying the first fraction by (x-2)/(x-2), the second fraction by (x+2)/(x+2), and the third fraction by x(x+2)/(x(x+2), we get:
(18(x-2))/(x(x-2)) + (14(x+2))/(x(x+2)) = 20/(x-2)
Expanding the fractions, we get:
(18x - 36)/(x^2 - 2x) + (14x + 28)/(x^2 + 2x) = 20/(x-2)
Combining the fractions, we get:
(32x - 8)/(x^2 - 4) = 20/(x-2)
Cross multiplying, we get:
20(x^2 - 4) = 32x - 8(x-2)
20x^2 - 80 = 32x - 8x + 16
20x^2 - 24x - 64 = 0
Dividing through by 4, we get:
5x^2 - 6x - 16 = 0
Solving this quadratic equation, we find two possible solutions:
x = 2 or x = -1.6
But, we need to check if these are valid solutions by plugging back into the original equation. After checking, we find that x = 2 is a valid solution.