Question

Fie expresia E(x) = $( \frac{x+1}{x} - \frac{x-1}{x+1} + \frac{1-x}{ x^{2} +x} ) : \frac{2x-4}{ x^{2} +3x}$

Answer 1

 Calculez mai intai paranteza:

(x+1)/x -(x-1)/(x+1) +(1-x)/(x^2 +x)=

(x+1)/x -(x-1)/(x+1) +(1-x)/x(x+1)=

Aducem la acelasi numitor:

(x+1)^2 /(x(x+1)) -x(x-1)/(x(x+1)) +(1-x)/(x(x+1))=

(x^2+2x+1-x^2+x+1-x)/(x(x+1))=

2(x+1)/(x(x+1))=

2/x

E(x)=(2/x)*x(x+3)/2(x-2)=(x+3)/(x-2)

E(x)=(x+3)/(x-2)

''^''=la puterea