Graphs and Transformations
Here’s an “ingelious” way to save time doing long division related to JC A Level H2 Mathematics Graphs and Transformation:
$\frac{x+2}{x-1} $
$= \frac {(x-1)+3}{x-1} $
$= 1 + \frac{3}{x-1} $
Next, consider
$\frac{2x+2}{x-1} $
$= \frac {2(x-1)+4}{x-1} $
$= 2 + \frac{4}{x-1} $
Next, consider
$\frac{2x^2+2}{x-1} $
$= \frac {2x(x-1)+2x+2}{x-1} $
$= 2x + \frac {2x+2}{x-1} $
$= 2x + \frac {2(x-1)+3}{x-1} $
$= 2x + 2 + \frac {3}{x-1} $
