Question

Fie expresia E(X)=$\frac{5}{ x^{2} +6} - \frac{4}{ x^{2} -5}$ aduceti expresia E(X)÷(2$x^{2}$+12)^-1 la forma cea mai simpla

Answer 1

E(x)=[5(x²-5) - 4(x²+6)]/(x²+6)(x²-5)
= (5x²-25-4x²-24)/(x²+6)(x²-5)
= (x²-49)/(x²+6)(x²-5)

E(x):(2x²+12)^(-1)=E(x)·(2x²+12)=2(x²+6)·E(x)=
=2(x²+6)·(x²-49)/(x²+6)(x²-5)=
=2(x²-49)/(x²-5)=
=2(x-7)(x+7)/(x²-5)