Question

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c) 2 + 1/x = 7/x d) 9/x + 6/x = 3 e) 8 – 3/x = 1/x f) (x +1)/ 3x + 1/x = ⅔ g) 3/4x – 3/5x + 1/10 = 0 h) (x -3) / (x + 3) = ⅗ i) 3x / (x – 4) -2/x = 3 j) (x + 7) / (x + 5) – 12/(x -5) = 1

Answer 1

c) 2 + 1/x = 7/x

MMC: X

2x + 1 = 7
2x = 7 - 1
2x = 6
x = 6/2 = 3

d) 9/x + 6/x = 3

MMC: x

9 + 6 = 3x
15 = 3x
x = 15/3 = 5

e) 8 - 3/x = 1/x

MMC: x

8x - 3 = 1
8x = 1 + 3
x = 4/8 = 1/2

f) (x+1)/3x + 1/x = 2/3

MMC: 3x

x+1 + 3.1 = 2x
1 + 3 = 2x - x
x = 4

g) 3/4x - 3/5x + 1/10 = 0

MMC: 20x

5.3 - 4.3 + 2x = 0
2x = -15 + 12
2x = -3
x = -3/2

h) (x-3)/(x+3) = 3/5

Multiplicar cruzado:

   5(x-3) = 3(x+5)
   5x - 15 = 3x + 15
   5x - 3x = 15 + 15
   2x = 30
     x = 30/2 = 15

i) 3x/(x-4) - 2/x = 3

MMC: (x-4).x

  3x.x - 2.(x-4) = 3(x-4)x
  3x² - 8x + 8 = 3x² - 12x
  3x² - 3x² + 12x - 8x = -8
   12x = -8
       x = -8/12 = -2/3

j) (x+7)/(x+5) - 12/(x-5) = 1

MMC: (x+5)(x-5)

(x+7)(x-5) -12(x+5) = 1(x+5)(x-5)
x² + 2x + 35 -12x - 60 = x² +10x + 25
x² - x² + 2x - 12x - 10x = 25 + 60 - 35
-20x = 50
x = 50/-20 =  -5/2