Simplifying rational expressions
● Simplifying rational expressions or algebraic fractions works in the same way as
simplifying normal fractions.
● A common factor must be found and divided throughout.
1) 3)
2)
,Simplifying rational expressions with factorising
● Some rational expressions do not have obvious common factors.
● In these cases, it is necessary to factorise either the numerator or the denominator, or both, to
find common factors.
1)
,Adding and subtracting rational expressions
● Adding and subtracting algebraic fractions is a similar process to
adding and subtracting normal fractions.
● Fractions can only be added or subtracted when there is a common denominator and algebraic fractions
are the same in this method.
1)
2)
,Multiplying and dividing rational expressions
● The method to multiply fractions is to multiply the numerators together, multiply the denominators together
and then cancel down if necessary.
● The method to divide fractions is to keep the first fraction the same, turn the divide sign into a multiply and
turn the second fraction upside down.
● This is known as multiplying by the reciprocal. The sum then becomes multiplying two fractions, which is
done using the method above.
1) 2)
,1) Exam questions
, 2)
● Simplifying rational expressions or algebraic fractions works in the same way as
simplifying normal fractions.
● A common factor must be found and divided throughout.
1) 3)
2)
,Simplifying rational expressions with factorising
● Some rational expressions do not have obvious common factors.
● In these cases, it is necessary to factorise either the numerator or the denominator, or both, to
find common factors.
1)
,Adding and subtracting rational expressions
● Adding and subtracting algebraic fractions is a similar process to
adding and subtracting normal fractions.
● Fractions can only be added or subtracted when there is a common denominator and algebraic fractions
are the same in this method.
1)
2)
,Multiplying and dividing rational expressions
● The method to multiply fractions is to multiply the numerators together, multiply the denominators together
and then cancel down if necessary.
● The method to divide fractions is to keep the first fraction the same, turn the divide sign into a multiply and
turn the second fraction upside down.
● This is known as multiplying by the reciprocal. The sum then becomes multiplying two fractions, which is
done using the method above.
1) 2)
,1) Exam questions
, 2)
