Question

Fie expresia E(X)=$\frac{4}{ X^{2}+8 } - \frac{3}{ X^{2}+5 }$
Aduceți expresia E(X):(2X²+16)^{-1} la forma cea mai simplă.

Answer 1

[tex]E(x)=\frac{4}{x^2+8}-\frac{3}{x^2+5}\\ E(x):(2x^2+16)^{-1}=\\ \left(\frac{4}{x^2+8}-\frac{3}{x^2+5}\right):\frac{1}{2(x^2+8)}=\\ \frac{4(x^2+5)-3(x^2+8)}{(x^2+8)(x^2+5)}\cdot 2(x^2+8)=\\ \frac{4x^2+20-3x^2-24}{x^2+5}\cdot 2=\\ \frac{2(x^2-4)}{x^2+5}=\boxed{\boxed{\frac{2(x-2)(x+2)}{x^2+5}}}[/tex]