Question

Calculati :

a) $[2x+[2x+( \frac{2x-1}{x-1} ) ^{-1} ]^{-1}]^{-1}$ , pentru x=$-\frac{1}{2}$

b) $\frac{ \frac{1}{3}- x^{-2} }{9- (\frac{1}{x}) ^{-2}}: [ \frac{1}{ 3^{-2} (3+x)}-3* x^{-1}-8 ]$ , pentru x=$-\frac{1}{3}$

Answer 1

a) se inlocuieste x cu -$\frac{1}{2}$ ; si rezulta :
$[ - \frac{2}{2} + [- \frac{2}{2} + ( \frac{- \frac{2}{2}-1}{- \frac{1}{2}-1}})^{-1} ]^{-1}]^{-1}$ 



[tex] [ - 1 + [- 1 + ( \frac{- 1-1}{- \frac{3}{2})^{-1} ]^{-1}]^{-1} = [ - 1 + [- 1 + ( \frac{-4}{3})^{-1} ]^{-1} ]^{-1} [/tex]



$[ - 1 + (- 1 + \frac{3}{4} )^{-1}]^{-1} = ( - 1 + \frac{-1}{4} )^{-1} = ( \frac{-4}{4} + \frac{-1}{4} )^{-1} = ( \frac{-5}{4})^{-1} = - \frac{4}{5}$