Answer :

Given:

taking LCM


cross multiplying


3x2 - 5x = 6x2 - 18x + 12


3x2 - 13x + 12 = 0


Using the splitting middle term - the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 3 b = - 13 c = 12


= 3.12 = 36


And either of their sum or difference = b


= - 13


Thus the two terms are - 9 and - 4


Sum = - 9 - 4 = - 13


Product = - 9. - 4 = 36


3x2 - 13x + 12 = 0


3 x2 - 9x - 4x + 12 = 0


3x (x - 3) - 4(x - 3) = 0


(x - 3) (3x - 4) = 0



Hence the roots of equation are


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