Question

(x-2)/(x+2)+(x+2)/(x-2)=2(x+3)/(x-3)​

Answer 1

Answer:

x = 3/4

Step-by-step explanation:

(x-2)/(x+2)+(x+2)/(x-2)=2(x+3)/(x-3)​

Taking L.C.M

{(x-2)(x-2) + (x+2)(x+2)} / (x+2)(x-2) = 2(x+3)/(x-3)​

{(x² + 4 - 4x) + (x² + 4 + 4x)} / (x² - 4) = (2x + 6)/(x-3)

(x² + 4 - 4x + x² + 4 + 4x) / (x² - 4) = (2x + 6)/(x-3)

(2x² + 8)/(x²  - 4) = (2x + 6)/(x-3)

cross-multiplying

(2x² + 8) (x-3) = (2x + 6)(x² - 4)

2x^3 + 8x - 6x² - 24 = 2x^3 + 6x² - 8x - 24

12x² = 16 x

12x = 16

x = 12/16

x = 3/4