Question

find the roots of the equation 1/x-1(x-2) =3;x≠0,2​

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)

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

2a

6±√[62-4(3)(2)]

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

2(3)

6±√(36-24)

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

6

6±√12

-------

6

6±2√3

-------

6

3±√3

------

3