A collection of resources for you to learn and practise algebraic fractions.
For a basic explanation see Mathisfun and note the questions to try at the end of that page.
The University of Hull Mathematics notes seem very clear, in the Algebra section we have clear notes and exercises with answers on Algebraic Fractons. The notes and exercises include adding, subtracting, multiplying and dividing algebraic fractions.
From the Centre for Innovation in Mathematics Teaching see section 10.13 of this chapter on equations for examples and exercises with algebraic fractions. You could check answers to the exercises on Wolfram Alpha. For example :