Solve the equation: `1/(x - 2) + (2x)/((x - 2)(x - 8)) = x/(2(x - 8))`

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The equation `1/(x - 2) + (2x)/((x - 2)(x - 8)) = x/(2(x - 8))` has to be solved.

`1/(x - 2) + (2x)/((x - 2)(x - 8)) = x/(2(x - 8))`

=> `(x - 8)/((x-8)(x - 2)) + (2x)/((x - 2)(x - 8)) = (x(x-2))/(2(x - 8)(x-2))`

=> `x - 8 + 2x = (x^2 - 2x)/2`

=> x^2 - 2x = 6x - 16

=> x^2 - 8x + 16 = 0

=> (x - 4)^2 = 0

=> x = 4

**The solution of the equation is x = 4.**

This will not an equation if x=2 and x=8. So to solve this we first assume

`x!=2,8`

`1/(x-2)+(2x)/((x-2)(x-8))=x/(2(x-8))`

LCM of {(x-2),(x-2)(x-8)}=(x-2)(x-8)

So, multiply both side by LCM

(x-8)+2x=x(x-2)/2

3x-8=x(x-2)/2

6x-16=x^2-2x

x^2-2x-6x+16=0

x^2-8x+16=0

(x-4)^2=0

x-4=0

x=4

Thus answer is x=4

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