Question

1/x-1=(3/x-2) -2/x-3
Sabendo que
X diferente de 1, 2 e 3

Answer 1

Resposta:

1 3 2

--------- = ( ------ ) - --------

x -1 x-2 x - 3

1(x-2)(x-3) 3(x-1)(x-3) 2(x+1)(x-2)

--------------------- = ------------------- - -------------------

x-1(x-2)(x-3) x-1(x-2)(x-3) x-1(x-2)(x-3)

x²-3x-2x+6= 3(x²-3x-x+3) - 2(x²-2x+x-2)

x²-5x+6= 3x²-9x-3x+9-2x²+4x-2x+4

x² - 5x + 6 = 3x² - 12x + 9 - 2x² + 2x + 4

x² - 3x² + 2x² - 5x + 12x - 2x + 6 - 9 - 4 = 0

5x - 7 = 0

5x = 7

x = 7/5