Question

Help me please ! I’ve tried a way but I don’t know if it’s correct. I want to see what you guys come up with.

Answer 1

`(3)/(x-2) + (8)/(x + 3) = 2` ; restriction is x ≠ 2, x ≠ -3

⇒
`((x+3)/(x+3) )(3)/(x - 2) + ((x - 2)/(x - 2))(8)/(x + 3) = (((x + 3)(x - 2))/((x + 3)(x - 2)) ) 2`

⇒ 3(x + 3) + 8(x - 2) = 2(x + 3)(x - 2)

⇒ 3x + 9 + 8x - 16 = 2(x² + x - 6)

⇒ 3x + 9 + 8x - 16 = 2x² + 2x - 12

⇒ 11x - 7 = 2x² + 2x - 12

⇒ 0 = 2x² - 9x - 5

⇒ 0 = (2x + 1)(x - 5)

0 = 2x + 1 , 0 = x - 5

-1 = 2x 5 = x

`-(1)/(2) = x`

Answer: {
`-(1)/(2)`, 5}