# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2012 | June | Q#3

Question

Show that  can be written in the form , where a and b are integers.

Solution

We are given;

If we need a rational number in the denominator of a fraction, we need to follow procedure of  “denominator rationalization” as given below.

ü If the denominator is of the form  then multiply both numerator and denominator by

ü If the denominator is of the form  then multiply both numerator and denominator by  .

ü If the denominator is of the form  then multiply both numerator and denominator by  .

We can expand and simplify the denominator as follows.

We have algebraic formula;