(sqrt(9 x^3)-5 x^(2+3))/(x-x^2)+4 x^(3)

To simplify the expression \( \frac{\sqrt{9 x^{3}-5 x^{2}+3}}{x-x^{2}+4 x^{3}} \), we need to analyze both the numerator and the denominator.<br /><br />The numerator is \( \sqrt{9 x^{3}-5 x^{2}+3} \).<br /><br />The denominator is \( x - x^2 + 4x^3 \).<br /><br />There are no common factors between the numerator and the denominator that can be simplified further. Therefore, the expression in its simplest form remains:<br /><br />\[ \frac{\sqrt{9 x^{3}-5 x^{2}+3}}{x-x^{2}+4 x^{3}} \]