4. Find roots of the equation `12((x)/(x-1)) + 12((x-1)/(x)) = 25`
` 12((x)/(x-1)) + 12((x-1)/(x)) = 25`
` "Let " (x)/(x-1) = m`
` => 12m + 12/m = 25`
` => 12m^2 - 25m + 12 = 0`
` => (12m^2-25m+12) = 0`
` => 12m^2-25m+12 = 0`
` => (12m^2-25m+12) = 0`
` => (12m^2-9m-16m+12) = 0`
` => 3m(4m-3)+(-4)(4m-3) = 0`
` => (3m-4)(4m-3) = 0`
` => (3m-4) = 0" or "(4m-3) = 0`
` => 3m = 4" or "4m = 3`
` => m = 4/3" or "m = 3/4`
` " Now," (x)/(x-1) = 4/3`
` => 3(x) = 4(x-1)`
` => 3(x) - 4(x-1) = 0`
` => (3x-4(x-1)) = 0`
` => (-x+4) = 0`
` => x = 4`
` " Now," (x)/(x-1) = 3/4`
` => 4(x) = 3(x-1)`
` => 4(x) - 3(x-1) = 0`
` => (4x-3(x-1)) = 0`
` => (x+3) = 0`
` => x = -3`
This material is intended as a summary. Use your textbook for detail explanation.
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