1ARationalFunctions

Breaking up Rational Functions

Consider the equation math y=\dfrac{x^2+2}{3x} math

To sketch this, we need to express it as the sum of 2 separate terms. math y=\dfrac{x^2+2}{3x} math

Split the fraction into two terms math y=\dfrac{x^2}{3x}+\dfrac{2}{3x} math

Simplify where possible math y=\dfrac{x}{3}+\dfrac{2}{3x} math

Now Sketch The equation is now ready to sketch by addition of ordinates.

It has a vertical asymptote at x = 0 and an oblique asymptote at y = x/3

Using the Classpad Calculator (The Specialist Maths text gives a more complicated way of doing this using Classpad in Eg 4)

The Classpad will split up a fraction for you.

Use the __**Expand**__ function in the ACTION menu TRANSFORMATION submenu. The fraction can be entered using the 2D tab of the virtual keyboard. math \text{Enter: } \; \textbf{Expand} \left( \dfrac{x^2+2}{3x} \right) math

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