Algebraic fractions

Algebraic fractions

1. simplify

   • Example
     • x² - 16 __________
       • x² + 2x - 8
         • (x + 4) (x - 4) __________
           • (x - 2) (x + 4)
             • x - 4 _______ x - 2
               • you can cancel out the two (x + 4) brackets because they are on the top and the bottom
                 • This is your answer
           • Factorise normally with quadratics
       • Simplify:
   • You simplify algebraic fractions by cancelling common terms on the top and bottom (you may have to factorise first)

2. add

   • Example
     • what is :
       • 3 ____ x+3
         • +
           • 1 ___ x-2
       • 3 (x-2) _______ (x+3) (x-2)
         • +
           • 1(x+3) _______ (x+3)(x-2)
             • creating the common denominator by timesing both parts of the first fraction by the denominator of the second, and multiplying both sections of the second fraction by the denominator of the first
         • 3x-6 _______ (x+3)(x-3)
           • +
             • x+3 _______ (x+3)(x-3)
               • simplified
           • 4x-3 ______ (x+3)(x-2)
             • This is the answer, we have dded the two numerators together and not changed the denominatoor
   • work out the common denominator. multiply the denominator and numerator of each fraction by whatever gives the common denominator
     • add or subtract the numerators only

3. divide

   • Example
     • x² -4 ________ x²+x -12
       • ÷
         • 2x + 4 ________ x² -3x
       • x² -4 ________ x²+x -12
         • x
           • x² -3x _______ 2x + 4
             • flip the second fraction, and change the divide to a multiply. then work the equation as a multiply shows to the left
   • To divide, flip the second fraction and then multiply as shown in the multiply section

4. multiply

   • Example
     • x² -4 ________ x² +x -12
       • x
         • x² -3x _______ 2x + 4
       • (x+2)(x-2) __________ (x+4)(x-3)
         • x
           • x(x-3) _______ 2(x+2)
             • factorise all the terms
         • (x-2) _____ (x+4)
           • x
             • x ___ 2
               • cancel all common terms
           • x(x - 2) ________ 2(x + 4)
             • this is your answer, when multiplying the numerators and denominators
   • multiply the numerators, and the denominators seperately