Question

Determine a solução da inequação:


1/1-2x > 1/2x + 1

Answer 1

Resposta:

Se for 1/(1-2x) >1/(2x+1)

1/(1-2x) - 1/(2x+1) > 0

(2x+1-1+2x)/(1-4x²) > 0

4x/(1-4x²) > 0

p=4x .....raiz x=0 ....   a=4>0  é  crescente

p------------------------------(0)+++++++++++++++++++++++++++++

q=1-4x²  ...x'=1/2 e x''=-1/2  ..........a=-4<0

q--------------(-1/2)+++++++(1/2)------------------------

Estudo de sinais:

p---------------------------(0)+++++++++++++++++++++++++++++++

q----------(-1/2)+++++++++++++++++++++(1/2)------------------------

p/q++++(-1/2)----------(0)+++++++++++++(1/2)------------------------

x< -1/2  U  0 <  x  <1/2