Answer:
See below
Explanation:
Let the original fraction be (x - 3) / x, then:
(x - 3) / x + (x - 3 + 2) / (x + 2) = 29/30
(x - 3) / x + (x - 1) / (x + 2) = 29/30
Multiply through by the LCD 30x(x + 2) we have:
30(x - 3)(x+ 2) + 30x (x - 1) = 29x(x + 2)
30(x^2 - x - 6) + 30x^2 - 30x = 29x^2 + 58x
30x^2 - 30x - 180 + 30x^2 - 30x = 29x^2 + 58x
60x^2 - 29x^2 - 60x - 58x - 180 = 0
31x^2 - 118x - 180 = 0
The solutions to this are not integers which makes me think there might be a mistake in the question...
The solutions of the last equation are x = 4.97 or -1.17.