For this case, we must resolve the following difference:
[tex]\frac {x + 5} {x + 2} - \frac {x + 1} {x ^ 2 + 2x} =\\\frac {(x + 5) (x ^ 2 + 2x) - (x + 2) (x + 1)} {(x + 2) (x ^ 2 + 2x)} =\\\frac {x ^ 3 + 2x ^ 2 + 5x ^ 2 + 10x- (x ^ 2 + x + 2x + 2)} {x ^ 3 + 2x ^ 2 + 2x ^ 2 + 4x} =\\\frac {x ^ 3 + 2x ^ 2 + 5x ^ 2 + 10x-x ^ 2-x-2x-2} {x ^ 3 + 2x ^ 2 + 2x ^ 2 + 4x} =[/tex]
Adding similar terms:
[tex]\frac {x ^ 3 + 7x ^ 2 + 10x-x ^ 2-3x-2} {x ^ 3 + 4x ^ 2 + 4x} =\\\frac {x ^ 3 + 6x ^ 2 + 7x-2} {x ^ 3 + 4x ^ 2 + 4x}[/tex]
Answer:
[tex]\frac {x ^ 3 + 6x ^ 2 + 7x-2} {x ^ 3 + 4x ^ 2 + 4x}[/tex]
