Asked by v8
What is the difference?
StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction
StartFraction 2 (x + 6) Over (x + 4) (x minus 4) EndFraction
StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction
StartFraction x minus 3 Over (x + 5) (x minus 4) EndFraction
StartFraction negative 2 (x minus 6) Over (x + 4) (x minus 4) EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Compute with common denominator (x-4)(x+4):
x/(x^2-16) - 3/(x-4)
= x/((x-4)(x+4)) - 3(x+4)/((x-4)(x+4))
= [x - 3(x+4)]/((x-4)(x+4))
= [-2x - 12]/((x-4)(x+4))
= -2(x+6)/((x+4)(x-4)).
So the correct choice is StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction. Domain: x ≠ 4, −4.
x/(x^2-16) - 3/(x-4)
= x/((x-4)(x+4)) - 3(x+4)/((x-4)(x+4))
= [x - 3(x+4)]/((x-4)(x+4))
= [-2x - 12]/((x-4)(x+4))
= -2(x+6)/((x+4)(x-4)).
So the correct choice is StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction. Domain: x ≠ 4, −4.
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