Question

Resolva as seguintes equações:

a)$\frac{x-2}{6x} = \frac{1}{x}$
b)$\frac{11}{x-4} +8= \frac{x}{x-4}$

Answer 1

a)

x - 2 = 1
  6x     x

x(x - 2) = 6x
x² - 2x = 6x
x² - 2x - 6x = 0
x² - 8x = 0

x(x - 8) = 0

x = 0

ou
x - 8 = 0
x = 8

Resp.: x = 0 e x = 8
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b)

  11   + 8  =   x     
x - 4             x - 4

mmc: (x - 4)

11 + 8.(x - 4) =     x   
    x - 4             x - 4

11 + 8x - 32 = x
11 - 32 + 8x = x
- 21 + 8x = x
- 21 = x - 8x
- 21 = - 7x  (-1)
21 = 7x
7x = 21
x = 21/7
x = 3

Resp.: x = 3