10 (a) If $P$ is irrational, show by the method of contradiction that $\frac{1}{P}$ is also irrational. (b) Give an example of two irrational numbers, $a$ and $b$, where $a \neq b$, such that $a b$ is rational.

$8 f(x)=\frac{3 x^{2}+16}{(1-3 x)(2+x)^{2}}=\frac{A}{(1-3 x)}+\frac{B}{(2+x)}+\frac{C}{(2+x)^{2}},|x|<\frac{1}{3}$. (a) Find the values of $A$ and $C$ and show that $B=0$. (b) Hence, or otherwise, find the series expansion of $f(x)$, in ascending powers of $x$, up to and including the term in $x^{3}$. Simplify each term. (7)

From the second image i want answer b part of question 8.

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