SOLUTION: Please help me to solve this problem: 4x^2-27x + 18 times x^2-2x-24 over over (x-6)^4 4x^2 + 13 x

SOLUTION: Please help me to solve this problem: 4x^2-27x + 18 times x^2-2x-24 over over (x-6)^4 4x^2 + 13 x - 12

Question 302100: Please help me to solve this problem:
4x^2-27x + 18 times x^2-2x-24
over over
(x-6)^4 4x^2 + 13 x - 12
Answer by london maths tutor(243) (Show Source): You can put this solution on YOUR website!
Factorise:
4x^2-27x + 18 = (4x - 3)(x-6)
(x-6)^4 = [(x-6)^2][(x-6)^2]
x^2-2x-24 = (x-6)(x+4)
4x^2+13x-12 = (4x-3)(x+4)
Putting the factorised bracket into the question, this gives:
[(4x - 3)(x-6)]/[(x-6)^2][(x-6)^2] * [(x-6)(x+4)]/(4x-3)(x+4)
you can cancel out (4x-3), (x-6) and (x+4)
This leaves: 1/[(x-6)^2]
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