Find the numerical value from the equation.

[ani22]

B) Given that 2x²-3/x²-4x+4 = 2 + A/x-2 + B/(x-2)²

(i) Find the numerical value of A and B.

(ii) Hence, or otherwise, determine the stationary points and the nature.

(iii) Determine the point of inflexion on the graph.

 

[Muddyakka]

(i) I am going to assume you mean (2x²-3)/(x²-4x+4)

Apply a long division of polynomials:
(2x²-3)/(x²-4x+4) = 2 + (8x-11)/(x-2)²

A common trick is to add and subtract numbers (which is hard to see unless someone shows you):

= 2 + (8x-16)/(x-2)² + 5/(x-2)²

(ii) Let y = (2x²-3)/(x²-4x+4) = 2 + A/x-2 + B/(x-2)²
Find y' and set to zero.

To find the nature, sub in values of y' before and after the stationary point.

(iii) Find y'' and set to zero. However you may need to check this is actually a point of inflexion by ensuring that the concavity actually changes .