Question

$E(x)=( \frac{x}{x+4} - \frac{2x+3}{x-4} - \frac{ x^{2} +10x-8}{16- x^{2} } ): \frac{10}{3x-12}$ , unde x ∈ R \{-4,4} . Arătați că E(x)=$- \frac{3}{2}$

Answer 1

[x/(x+4)-(2x+3)/(x-4)-(x²+10x-8)/(16-x²)] : 10/(3x-12)=
={[x(x-4)-(2x+3)(x+4)+(x²+10x-8)]/(x-4)(x+4)} : 10/3(x-4)=
=[(x²-4x-2x²-3x-8x-12+x²+10x-8)/(x-4)(x+4) × 3(x-4)/10=
=(-5x-20)/(x+4) × 3/10=
=-5(x+4)/(x+4) × 3/10=
=- 3/2