Asked by Sham

(x-2)+1/x+1=2/3
Answered by Reiny
the way you typed it:
(x-2)+1/x+1=2/3
x-2 + 1/x + 1 = 2/3
x + 1/x -1 - 2/3 = 0
times 3x
3x^2 + 3 - 3x - 2x = 0
3x^2 - 5x + 3 = 0
x = (5 ± √-11)/6
no real solution

You probably meant:
x- 2 + 1/(x+1) = 2/3
times 3(x+1)
3x(x+1) - 6(x+1) + 3 = 2(x+1)
3x^2 + 3x - 6x - 6 + 3 = 2x + 2
3x^2 - 5x -5 = 0
x = (5 ±√85)/6

Why did you put brackets around x-2, which were not needed, and missed the ones where it counted ?
Answered by Lilinau
Heres my take....first combine like terms on the left side of equ......x-1/x+1 = 2/3
Now cross mult..... 3(x-1) = 2(x+1)

Distribute.....3x-3 = 2x +2
Subtr.....3x - 2x = 2 + 3
Yields....x = 5

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