Algebraic Fractions : Theory

• • To add and subtract algebraic fractions, they must have the same denominator 
  • To do this, you multiply the fraction on the left by the denominator of the fraction on the right 
  • Then, you multiply the fraction on the right by the denominator of the fraction on the left 
  • The fraction on the left, and the fraction on the right will both have the same denominators 
  • Then, you can add the 2 fractions

  
• • To multiply algebraic fractions, you multiply the numerators , and multiply the denominators 
  • You then write the multiplied numerators over the multiplied denominators 
  • You can then simplify the algebraic fraction (if there is a common term on the both the number and denominator) - You can also do this before you multiply the fractions

  
• • Sometimes, you may need to multiply algebraic fractions that have quadratics 
  • To do this, you would factorise the quadratics into brackets, and then multiply - do not expand the brackets when you do this 
  • You would then simplify the resulting fraction, by getting rid of / cancelling the terms that are in both the numerator and the denominator 
  • Remember - if all of the terms on either the numerator or denominator cancel, you are left with 1

  
• • To divide algebraic fractions, you multiply the first fraction by the reciprocal of the second fraction 
  • This means that you keep the first fraction the same, and flip the second fraction 
  • You then multiply the 2 fractions, and then cancel down / simplify where necessary

  
• • Sometimes, you may have to divide algebraic fractions that have quadratics 
  • Firstly, you factorise the quadratics into brackets - do not flip the second fraction before this 
  • Once this is done, then you flip the second fraction, and multiply - do not expand the brackets when you do this 
  • Then, you cancel down the like terms, and write the remaining fraction