4) Simplify. Write your answer using whole numbers and variables. (23q)/(9q^2)-4q square

To simplify the expression \(\frac{23q}{9q^2 - 4q}\), we first factor the denominator.<br /><br />The denominator \(9q^2 - 4q\) can be factored by taking out the common factor \(q\):<br />\[ 9q^2 - 4q = q(9q - 4) \]<br /><br />Now, we rewrite the original expression using this factorization:<br />\[ \frac{23q}{9q^2 - 4q} = \frac{23q}{q(9q - 4)} \]<br /><br />Next, we can cancel the common factor \(q\) in the numerator and the denominator:<br />\[ \frac{23q}{q(9q - 4)} = \frac{23}{9q - 4} \]<br /><br />Thus, the simplified form of the given expression is:<br />\[ \boxed{\frac{23}{9q - 4}} \]