Question

Simplificati raportul si stabiliti domeniul lui de definitie:

(x la puterea a 3a-2x patrat-x+2)/(2•x la puterea a 3a+3x patrat-8x-12)
Ajutorr!

Answer 1

se pune conditia de existenta a fractiei
2x³+3x²-8x-12≠0
2x(x²-4)  + 3(x²-4)=(x-2)(x+2)(2x+3)≠0
x≠{-2,-2/3, 2}
(x³-2x²-x+2)/(x-2)(x+2)(2x+3)
x³-2x²-x+2=x(x²-1)-2(x²-1)=(x-1)(x+1)(x-2)
(x-1)(x+1)(x-2)/(x-2)(x+2)(2x+3)=
(x-1)(x+1)/(x+2)(2x+3)