Asked by ryan
simplify this (x^2+5x+6)/(x^2-9)/(6x+9)/(12x^2)
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the expression as ((x^2+5x+6)/(x^2-9))/(6x+9)/(12x^2). Factor and simplify:
x^2+5x+6 = (x+2)(x+3)
x^2-9 = (x-3)(x+3)
6x+9 = 3(2x+3)
12x^2 = 12 x^2
So
((x+2)(x+3))/((x-3)(x+3) · 3(2x+3) · 12x^2)
= (x+2)/(36 x^2 (x-3)(2x+3)).
Keep the original exclusions: x ≠ 3, −3, −3/2, 0 (these make an original denominator zero).
x^2+5x+6 = (x+2)(x+3)
x^2-9 = (x-3)(x+3)
6x+9 = 3(2x+3)
12x^2 = 12 x^2
So
((x+2)(x+3))/((x-3)(x+3) · 3(2x+3) · 12x^2)
= (x+2)/(36 x^2 (x-3)(2x+3)).
Keep the original exclusions: x ≠ 3, −3, −3/2, 0 (these make an original denominator zero).
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