Question

Se considera expresia: E(x)= $( \frac{1}{2x+1} - \frac{1}{1-2x} - \frac{6x}{4 x^{2} -1} ) : ( \frac{4 x^{2} -1}{8x} ) x^{1} . \frac{4x}{ x^{2} +3x}$ 
a) Determinati x apartine R pentru care expresia este definita
b) Aduceti expresia la forma cea mai simpla
c) Calculati E$(\sqrt{3} -3 )$

Answer 1

a) x∈R\{-$\frac{1}{2}$;$\frac{1}{2}$;0;$\frac{1}{8}$} cred ca asa este aici 
b)E(x)=[tex]( \frac{2x-1+2x-1-6x}{4 x^{2}-1 }): \frac{4 x^{2}-1 }{8x}*x* \frac{4x}{x(x+3)} [/tex]
E(x)=$\frac{-2x}{4 x^{2}-1 }* \frac{4 x^{2}-1 }{8} * \frac{4}{x(x+3)}$
E(x)=$\frac{-2x}{2x(x+3)} => E(x)= \frac{-1}{x+3}$
c) E($\sqrt{3}$-3) = $\frac{-1}{ \sqrt{3}-3+3 } = \frac{-1}{ \sqrt{3} } = \frac{- \sqrt{3} }{3}$