A level revision

Solving algebraic fractions

It's recommended you recap handling rational and alegbraic expressions before revising this topic.

Solving equations involving algebraic fractions is pretty easy, you want to clear the fractions, expand any brackets, collect like terms and then attempt to solve the final equation either by factorisation or by inspection. The best way to revise is an example.

Example question: Solve the equation

Worked solution: Firstly you want to subtract the fractions on the left by giving them same denominator (revise this technique):



Now clear the fractions by multiplying each side by



Next, expand all the brackets:



Collect like terms and move them all to one side of the equation to leave you with 0 on the other:



From here, factorise:



Hence, 5x + 2 = 0 or -x + 3 = 0, so solve both these equations to get the two solutions:





And these are the final answers to the original question. As you can see there are a number of steps involved and so these questions are typically worth 5-7 marks.