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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