\frac { 1 } { x } - \frac { 1 } { x - 2 } = 3 ( x \neq 0,2 )
Answers
Answer:
x = (3+√3) / 3 , (3-√3) / 3
Step-by-step explanation:
We have
(1/x) - [1/(x-2)] = 3
Then,
1 1
=> --- - ------ = 3
x x - 2
The common denominator is x(x-2)
Thus =>
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
=> 3x^2 - 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
Hence, the values of x are :
x = (3+√3) / 3 , (3-√3) / 3