solve the algebraic inequality by wavy curve method

(a) (x²-5x+12)/(x²-4x+5) >3 answer: (1/2,3)

The discrimenant of the Quad. equation given in denomitor is < 0 and coeff. of x² is >0. This means that expression in denominator will always give the positive value. So now in this case we can cross multiply on the other side with 3.
So, x² – 5x + 12 > 3(x2 – 4x + 5)
or 2x² – 7x + 3 < 0
or (2x-1) (x-3) < 0
From here using wave curve method, x will belongs in between (1/2 , 3)

Thanks