Find naturals numbers $p$ and $q$ such that $\frac{\sqrt{p^2+7}}{\sqrt{q^2-3}}$ is rational
i have taken $$\frac{\sqrt{p^2+7}}{\sqrt{q^2-3}}=\frac{a}{b}$$ where $a$ and $b$ are positive integers which are co prime then after simplification we get
$$3a^2+7b^2=(aq-bp)(aq+bp)$$
$$3(a^2+b^2)+4b^2=(aq-bp)(aq+bp)$$
Obviously $a$ and $b$ both cannot be even since they are co prime
but now if i consider other cases i could not find $p$ and $q$...i will be happy if i get any hint