3. Find roots of the equation `12((2x+1)/(x-1))^2 + -5((2x+1)/(x-1)) + -2 = 0`

` 12((2x+1)/(x-1))^2 - 5((2x+1)/(x-1)) - 2 = 0`

` "Let " (2x+1)/(x-1) = m`

` => (12m^2-5m-2) = 0`

` => 12m^2-5m-2 = 0`

` => (12m^2-5m-2) = 0`

` => (12m^2+3m-8m-2) = 0`

` => 3m(4m+1)+(-2)(4m+1) = 0`

` => (3m-2)(4m+1) = 0`

` => (3m-2) = 0" or "(4m+1) = 0`

` => 3m = 2" or "4m = -1`

` => m = 2/3" or "m = -1/4`

` "Now, " (2x+1)/(x-1) = 2/3`

` => 3(2x+1) = 2(x-1)`

` => 3(2x+1) - 2(x-1) = 0`

` => (3(2x+1)-2(x-1)) = 0`

` => (4x+5) = 0`

` => 4x = -5`

` => x = -5/4`

` "Now, " (2x+1)/(x-1) = -1/4`

` => 4(2x+1) = -1(x-1)`

` => 4(2x+1) + 1(x-1) = 0`

` => (4(2x+1)+(x-1)) = 0`

` => (9x+3) = 0`

` => 9x = -3`

` => x = -3/9`

` => x = -1/3`

---

---