Partial fractions before a local expansion

Express $f(x)=\dfrac{3x^2-3x+4}{(2x-1)(x^2+3)}$ in partial fractions and hence obtain $f(x)$ as a series expansion in ascending powers of $x$ up to and including the term in $x^2$.5 marks

Find the range of values of $x$ for which the expansion is valid.1 mark