Problem

We know that
start fraction, 3, divided by, 1, plus, 3, x, end fraction, equals, 3, minus, 9, x, plus, 27, x, start superscript, 2, end superscript, minus, 81, x, start superscript, 3, end superscript, plus, point, point, point
for x(13,13)\displaystyle x\in\left(-\frac{1}{3},\frac{1}{3}\right).
Using this fact, find the function that corresponds to the following series.
3, x, minus, start fraction, 9, divided by, 2, end fraction, x, start superscript, 2, end superscript, plus, 9, x, start superscript, 3, end superscript, minus, start fraction, 81, divided by, 4, end fraction, x, start superscript, 4, end superscript, plus, point, point, point
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