Now, rewrite the equation in terms of the common denominator:
(3(x+2) - 6)/x(x+2) = 8/ (x+2)(x-2)
Expand and simplify the left side of the equation: (3x + 6 - 6) = 8/(x+2)(x-2) 3x = 8/(x+2)(x-2)
Now, multiply both sides by (x+2)(x-2) to get rid of the denominator: 3x(x+2)(x-2) = 8 3x(x^2 - 4) = 8 3x^3 - 12x = 8
Rearrange the equation: 3x^3 - 12x - 8 = 0
[This is a cubic equation, and can be solved using various methods such as graphing, numerical methods, or algebraic methods like synthetic division or factor theorem.]
It can be further simplified or solved using any preferred method.
To solve this equation, we first need to find a common denominator for all fractions involved:
3/x - 6/ x(x+2) = 8/ x^2 - 4
3/x - 6/ x(x+2) = 8/ (x+2)(x-2)
Now, rewrite the equation in terms of the common denominator:
(3(x+2) - 6)/x(x+2) = 8/ (x+2)(x-2)
Expand and simplify the left side of the equation:
(3x + 6 - 6) = 8/(x+2)(x-2)
3x = 8/(x+2)(x-2)
Now, multiply both sides by (x+2)(x-2) to get rid of the denominator:
3x(x+2)(x-2) = 8
3x(x^2 - 4) = 8
3x^3 - 12x = 8
Rearrange the equation:
3x^3 - 12x - 8 = 0
[This is a cubic equation, and can be solved using various methods such as graphing, numerical methods, or algebraic methods like synthetic division or factor theorem.]
It can be further simplified or solved using any preferred method.