and \(\dfrac{3}{2} = \dfrac{15 ... used for multiplying or dividing algebraic fractions is similar to the method for numerical fractions. However some expressions may need to be factorised ...

Parsing algebraic expressions is always a pain ... which has a nice flowchart and an example step-by-step parse of 1+2-3*4+5/6^7-8*9. Towards the bottom, there’s a nice animated flow chart ...