Question

una solucion de 1/x+1/x-1=8/3

Answer 1

1/(x+1/x-1) = 8/3
(x-1)/(x+1) = 8/3
3(x-1) = 8(x+1)
3x - 3 = 8x + 8
-5x = 11
x= 11/-5 = -(11/5)

Answer 2

1/x + 1/(x-1) = 8/3

(x-1+x) / x(x-1) = 8/3

(2x - 1) / x(x-1) = 8/3

3(2x-1) = 8x(x-1)

6x - 3 = 8x² - 8x

8x² - 14x + 3 = 0

(4x - 1)(2x - 3) = 0

x = 1/4 ó x = 3/2