Problem: fraction with equals answer
x-4 over x+1=x+3 over x+2
(x - 4)/(x + 1) = (x + 3)/(x + 2)
(((x + 1)(x + 2)) * ((x - 4)/(x + 1)) = (((x + 1)(x + 2)) * ((x + 3)/(x + 2))
(x + 2) * (x - 4) = (x + 1) * (x + 3)
x^2 + 2x - 4x - 8 = x^2 + x + 3x + 3
x^2 - 2x - 8 = x^2 + 4x + 3
x^2 - 2x - 8 - x^2 - 4x = x^2 + 4x + 3 - x^2 - 4x
-6x - 8 = 3
-6x - 8 + 8 = 3 + 8
-6x = 11
-6x/-6 = 11/-6
x = -11/6
Check.
(x - 4)/(x + 1) = (x + 3)/(x + 2)
((-11/6) - 4)/((-11/6) + 1) = ((-11/6) + 3)/((-11/6) + 2)
(-35/6)/(-5/6) = (7/6)/(1/6)
7 = 7
Answer: x = -11/6