Question

Dau 100 de puncte doar ajutati ma va rog !
E(x)= (x/x+4 - 2x+3/x-4-x la puterea a 2 a +10x-8/16-x la puetrea a 2 )
Aratati ca E(x)= - 3 supra 2
Va rog

Answer 1

Răspuns:

E(x) = x/(x+4) - (2x+3)/(x-4) - (x²+10x-8)/(16-x²)

= x/(x+4) - (2x+3)/(x-4) - (x²+10x-8)/(4-x)(4+x)

= x/(x+4) - (2x+3)/(x-4) + (x²+10x-8)/(x-4)(x+4)

= [x(x-4) - (x+4)(2x+3) + x² + 10x - 8]/(x-4)(x+4)

= (x² - 4x - 2x² - 11x - 12 + x² + 10x - 8)/(x-4)(x+4)

= (-5x - 20)/(x-4)(x+4)

= - 5(x + 4)/(x-4)(x+4)

= - 5/(x - 4)