(7 x^3-5 x^2+6)/(7 x-3 x^2)+9 x^(3)=

To simplify the expression \(\frac{4x^3 - 5x^2 + 6}{7x - 3x^2 + 9x^3}\), we first observe that both the numerator and the denominator are polynomials. <br /><br />The numerator is \(4x^3 - 5x^2 + 6\) and the denominator is \(7x - 3x^2 + 9x^3\). We can rewrite the denominator in standard form by arranging the terms in descending order of powers of \(x\):<br /><br />\[9x^3 - 3x^2 + 7x.\]<br /><br />Now, let's factor out the greatest common factor from both the numerator and the denominator if possible:<br /><br />1. **Numerator**: \(4x^3 - 5x^2 + 6\)<br /> - There is no common factor for all terms.<br /><br />2. **Denominator**: \(9x^3 - 3x^2 + 7x\)<br /> - The common factor here is \(x\), so we can factor it out:<br /> \[x(9x^2 - 3x + 7).\]<br /><br />Since there are no common factors between the numerator and the denominator, the expression cannot be simplified further by canceling terms. Therefore, the simplified form of the expression remains:<br /><br />\[\frac{4x^3 - 5x^2 + 6}{9x^3 - 3x^2 + 7x}.\]