Question

Fie expresia E = $\frac{1}{a+b} : \frac{3a-5}{a^2-b^2} + \frac{a+b}{3a-5}$
a) Aduceti la o forma mai simpla expresia.
b) Determinati DVA a raportului obtinut.
c) Determinati E(2).

Answer 1

E=1/(a+b):(3a-5)/(a²-b²)+(a+b)/(3a-5)=
=1/(a+b)×(a-b)(a+b)/(3a-5)+(a+b)/(3a-5)=
=(a-b)/(3a-5)+(a+b)/(3a-5)=
=(a-b+a+b)/(3a-5)
=2a/(3a-5)
 
a≠5/3   a ∈ R \ {5/3}

E(2)=2×2/(3×2-5)=4/(6-5)=4