simplify 6x/x+3=9/x-3-15/x^2-9

Question

please simplify

Answer 1

 

6x / (x + 3) = [9 / (x - 3)] - [15 / (x^2 - 9)]

6x(x - 3) / (x + 3)(x - 3) = [9(x + 3) / (x + 3)(x - 3)] - [15 / (x^2 - 9)]

(6x^2 - 18x) / (x^2 - 9) = [(9x + 27) / (x^2 - 9)] - [15 / (x^2 - 9)]

6x^2 - 18x = 9x + 27 - 15

6x^2 - 18x - 9x - 12 = 0

6x^2 - 27x - 12 = 0

2x^2 - 9x - 4 = 0

2(x^2 - (9/2)x) - 4 = 0

2(x - (9/4))^2 - (81/8) - 4 = 0

2(x - (9/4))^2 = 113 / 8

(x - (9/4))^2 = 113 / 16

x - 9/4 = sqrt(113 / 16) or = -sqrt(113 / 16)

x = 9/4 + sqrt(113 / 16) or x = 9/4 - sqrt(113 / 16)