Question

1by x minus 1by x-2=3,xis not equal to 0,2 find the roots of the following equations​

Answer 1

We have:

 

(1/x) - [1/(x-2)] = 3

 

1              1

---   -    ------  =  3

x            x-2

The common denominator is x(x-2)

 

1      x-2        1       x

---• -----  -  ----- • ---  = 3

x      x-2       x-2     x

x-2           x

-------  - -------  = 3

x(x-2)     x(x-2)

 

x-2 - x

--------  = 3

x(x-2)

-2 = 3x(x-2)

-2 = 3x²-6x

3x²-6x+2 = 0

Using the quadratic formula we can solve for x

-b±√(b²-4ac)

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

  6±√[6²-4(3)(2)]

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

    2(3)

 

6±√(36-24)

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

      6  

6±√12

-------

  6

 

 3±√3

------

  3  

Answer 2

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