### If x + y - 4t = 0 then find the value of $\dfrac{ x } { x - 2t } + \dfrac{ 2t } { y - 2t}$.

1

Step by Step Explanation:
1. We are given x + y - 4t = 0
It can also be written as: (x - 2t) + (y - 2t) = 0
or (x - 2t) = -(y - 2t)
2. The above step tells us that we may replace (x - 2t) with -(y - 2t) wherever needed.
3. We need to find the value of $\dfrac{ x } { x - 2t } + \dfrac{ 2t } { y - 2t}$ which is equal to:

 x -(y - 2t)
+
 2t y - 2t

=
 -x + 2t y - 2t

=
 -(x - 2t) (y - 2t)

4. As we know that (x - 2t) = -(y - 2t), the answer to the above question becomes 1.