Algebra: A Combined Approach (4th Edition)

$\dfrac{7}{6p^{2}+q}\div\dfrac{14}{18p^{2}+3q}=\dfrac{3}{2}$
$\dfrac{7}{6p^{2}+q}\div\dfrac{14}{18p^{2}+3q}$ Take out common factor $3$ from the denominator of the second fraction: $\dfrac{7}{6p^{2}+q}\div\dfrac{14}{18p^{2}+3q}=\dfrac{7}{6p^{2}+q}\div\dfrac{14}{3(6p^{2}+q)}=...$ Evaluate the division of the two rational expressions and simplify by removing repeated terms in the numerator and the denominator: $...=\dfrac{21(6p^{2}+q)}{14(6p^{2}+q)}=\dfrac{21}{14}=\dfrac{3}{2}$