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`
This material is intended as a summary. Use your textbook for detail explanation.
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