Show that if x is small compared with unity, then $$f(x)=\frac{(1-x)^\frac{-2}{3}+(1-4x)^\frac{-1}{3}}{(1-3x)^\frac{-1}{3}+(1-4x)^\frac{-1}{4}}=1-\frac{7x^2}{36}$$
In my first attempt I expanded all four brackets up to second order of x, but this didn't lead me to something that could be expressed as the final result. In my second attempt I decided to find $f'(x)$ and $f''(x)$ and use these to find $f'(0)$ and $f''(0)$ to find the Maclaurin expansion of $f(x)$ but this was way too time consuming. Can someone lead me to right track and offer some assistance? Thank you