D) Divide. Write your answer in simplest form. (q)/(25q^2)-30q+9div (q)/(5q-3) square

To divide the given fractions, we can multiply the first fraction by the reciprocal second fraction. <br /><br />$\frac {q}{25q^{2}-30q+9}\div \frac {q}{5q-3}$<br /><br />This is equivalent to:<br /><br />$\frac {q}{25q^{2}-30q+9} \times \frac {5q-3}{q}$<br /><br />Now, let's simplify the expression:<br /><br />$\frac {q(5q-3)}{q(25q^{2}-30q+9)}$<br /><br />We can cancel out the common factor of $q$ in the numerator and denominator:<br /><br />$\frac {5q-3}{25q^{2}-30q+9}$<br /><br />Therefore, the simplest form of the given expression is $\frac {5q-3}{25q^{2}-30q+9}$.