Question

G-ul va rog frumos!
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Answer 1

Răspuns:

x ∈ (-5/14 ; 2)

Explicație pas cu pas:

5x/(x-2) + 1 < 4/3 - 1/(x-2) <=>

³⁾5x/(x-2) + ³⁾1/(x-2) + ³⁾(x-2)/(x-2) - 4(x-2)/[3(x-2)] < 0 <=>

(15x+3+3x-6-4x+8)/[3(x-2)] < 0 <=>

(14x+5)/[3(x-2)] < 0

                     x I -∞         -5/14         2         +∞

             14x+5 I -------------  0 +++++++++++++

                 x-2 I---------------------------0+++++++

(14x+5)/[3(x-2)] I +++++++++0---------I++++++++ =>

x ∈ (-5/14 ; 2)