Answer
$1-\dfrac{3}{4}x^3+\dfrac{9x^6}{16}-\dfrac{27x^9}{64}+\dfrac{81x^{12}}{256}$
Work Step by Step
Since, we know $\dfrac{1}{1-x}=\Sigma_{n=0}^\infty x^n=1+x+x^2+x^3+x^4+...$
Now, $\dfrac{1}{1+\dfrac{3}{4}x^3}=\dfrac{1}{1-(-\dfrac{3}{4}x^3)}$
or, $=1+(-\dfrac{3}{4}x^3)+(-\dfrac{3}{4}x^3)^2+(-\dfrac{3}{4}x^3)^3+(-\dfrac{3}{4}x^3)^4+...$
or, $=1-\dfrac{3}{4}x^3+\dfrac{9x^6}{16}-\dfrac{27x^9}{64}+\dfrac{81x^{12}}{256}$
