Mathematics

Problem

Let

P=\dfrac{\sqrt{3}}{7-2\sqrt{3}}

and

Q=\dfrac{3\sqrt{3}}{7+2\sqrt{3}}

. a. (i) Rationalise the denominator of

P

and simplify your result. b. (ii) Rationalise the denominator of

Q

and simplify your result. c. (iii) Hence, or otherwise, find the exact value of

P+Q