Answer:
The solution set is {-2/9, 4).
Step-by-step explanation:
(x + 3)/(x-2) - (1-x)/x = 17/4
Multiply through by the LCD ( = 4x(x - 2):
(x + 3)4x - 4(1 - x)(x - 2) = 17x(x - 2)
4x^2 + 12x - 4(x - 2 - x^2 + 2x) - 17x^2 + 34x = 0
4x^2 + 12x - 4x + 8 + 4x^2 - 8x - 17x^2 + 34x = 0
-9x^2 + 34x + 8 = 0
We need 2 numbers whose product = -72 ( -9 * 8) and whose sum is 34.
These are +36 and -2, so we write:
-9x^2 + 36x - 2x + 8 = 0
-9x(x - 4) - 2(x - 4) = 0
(-9x + 2)(x - 4) = 0
x = -2/9, 4.
