Question

# Evaluate

Since at  numerator and denominator becomes zero.
∴ it  is of   form.
∴ By factor theorem,  is a factor of both numerator and denominator.
is also a factor of both numerator and denominator because irrational roots occur in pairs.
So, x-2 is a factor of both numerator and denominator.
By long division method, dividing numerator and denominator by x-2.
x- 3x+ x- 9x- 4x- 16x + 84 = (x-2) (x- 3x+ 2x-5x+ 4x-19x+8x - 42)  and  x5-3x-4x + 12 = (x-2) (x- 3x+ 2x -6)

∴