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Factor the denominators
Multiply by common denominator x(x+1)(x+2), Cancel the denominaors, results:
(x+1)(x+1) - (x+2)(x+4) = -3x
FOIL
x^2 + 2x +1 - (x^2 + 6x + 8) = -3x
remove the brackets change the signs
x^2 + 2x +1 - x^2 - 6x - 8 = -3x
Combine like terms
x^2 - x^2 + 2x - 6x + 3x + 1 - 8 = 0
-x - 7 = 0
-x = +7
x = -7
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You can confirms this by replacing x with -7 in the original problems