Question

Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared plus 12 x plus 36 over quantity x plus 6.

Answer 1

I am unsure as to whether it is x+6/x-9 or (x+6)^2/x-9

Answer 2

We start with: \[\frac{ x^2 - 3x - 54 }{ x^2 - 18x + 81 }\times \frac{ x^2 + 12x + 36 }{ x + 6 }\]
Factoring each of these polynomial expressions gets us the following: \[\frac{ (x-9)(x+6)(x+6)(x+6) }{ (x-9)(x-9)(x+6) }\] which quickly condenses to: \[\frac{ (x-9)(x+6)^3 }{ (x-9)^2(x+6) }\] Because of all the common factors in the numerator and denominator, we can reduce this further to our final and most reduced form: \[\frac{ (x+6)^2 }{ x-9 }\] which is our final answer.