How do you simplify # [(x^2 - 2x - 15) / [(x - 6)(x - 3)]] * [(x^2 - 6) / (x - 5)]#?

1 Answer
Jul 18, 2017

Answer:

Factorise, multiply then simplify.

Explanation:

  1. Factorise all statements that can be factorised.
    #x^2-2x-15 = (x+3)(x-5)#
    #x^2-6 = (x+sqrt(6))(x-sqrt(6))#

  2. Then multiply the two brackets. Remember to multiply fractions multiply the numerators by each other and repeat with denominators.
    #((x+3)(x-5)(x+sqrt(6))(x-sqrt(6)))/((x-6)(x-3)(x-5))#

  3. Simplify by removing like terms in the numerator and denominator.
    #((x+3)(x+sqrt(6))(x-sqrt(6)))/((x-6)(x-3))#

I know it looks complicated but it is fully simplified, hope this has helped.