(3x/x+1) - (4/x+2) = -3/x^2+3x+2

Question

I really don't understand, but I got 1/3

Answer 1

x^2 + 3x + 2 factors to (x + 1) (x+2)

multiply all terms by (x+1)(x+2) to clear denominators from all terms:

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

3x^2 + 6x - 4x - 4 = -3

3x^2 + 2x -1 = 0

3x^2 + 3x - x - 1 = 0

3x (x + 1) - (x + 1) = 0

(x+1)(3x-1) = 0

x+1 = 0 or 3x-1 = 0

x = -1 or 1/3

can only be x = 1/3 because x = -1 would produce 0 in the denominator which is undefined.