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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