Question

1÷(x-1)(x-2) + 1÷(x-2)(x-3) = 2÷3 find x

Answer 1

Answer:

Step-by-step explanation:

   1            +       1            =   2 

---------------    ----------------     ----

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

   1    [     1     +     1     ]  =  2 -------------[Taken 1 / (x - 2) Common ]

-------   ---------    ---------      ----

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

  

  1     [x - 3 + x - 1]  = 2 

-------  ------------------  ----

(x - 2)  (x - 1)(x  -  3)   3

  

  1     [   2x - 4   ]   = 2 

-------   -------------     ----

(x - 2)  x² - 4x + 3      3

 

       2x - 4                   =  2

----------------------------     -----

x³ - 4x² - 2x²  + 3x - 6       3

       2x - 4             =  2

----------------------      -----

x³ - 6x² + 3x - 6         3

(2x - 4)3 = 2(x³ - 6x² + 3x - 6)

6x -12 = 2x³ -12x² +6x -12--[6x - 12 gets cancelled on both the sides]

2x³ - 12x² = 0

2x²( x - 6 ) = 0

2x² = 0  OR x - 6 = 0

x = 0     OR  x = 6

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