Would recommend reading this excellent post by Jo Morgan for more on the inspiration behind this exercise!
Algebraic LCM (pdf)
Algebraic LCM (doc)
A more introductory set of questions on simplifying algebraic fractions – no knowledge of quadratics is required.
Simplifying Algebraic Fractions (pdf)
Simplifying Algebraic Fractions (doc)
Students do not need to expand double brackets/factorise quadratic expressions to access these.
Multiplying/Dividing Algebraic Fractions – pdf
Multiplying/Dividing Algebraic Fractions – doc