2023 SCSS P1 Q8

Show that \(\dfrac{\sqrt3+2}{5\sqrt3-1}\) can be written in the form of \(\dfrac{a+b\sqrt3}c\) where \(a\), \(b\) and \(c\) are integers.[4]

It is given that \(\sqrt7(x+2)=1-x\). Find \(x\) in the form \(p+q\sqrt7\), where \(p\) and \(q\) are rational numbers.[4]