Question

What is the difference x + 5/ x + 2 - x + 1 /x^2 + 2x

Answer 1

For this case, we must resolve the following difference:

$\frac {x + 5} {x + 2} - \frac {x + 1} {x ^ 2 + 2x} =\\\frac {(x + 5) (x ^ 2 + 2x) - (x + 2) (x + 1)} {(x + 2) (x ^ 2 + 2x)} =\\\frac {x ^ 3 + 2x ^ 2 + 5x ^ 2 + 10x- (x ^ 2 + x + 2x + 2)} {x ^ 3 + 2x ^ 2 + 2x ^ 2 + 4x} =\\\frac {x ^ 3 + 2x ^ 2 + 5x ^ 2 + 10x-x ^ 2-x-2x-2} {x ^ 3 + 2x ^ 2 + 2x ^ 2 + 4x} =$

Adding similar terms:

$\frac {x ^ 3 + 7x ^ 2 + 10x-x ^ 2-3x-2} {x ^ 3 + 4x ^ 2 + 4x} =\\\frac {x ^ 3 + 6x ^ 2 + 7x-2} {x ^ 3 + 4x ^ 2 + 4x}$

Answer:

$\frac {x ^ 3 + 6x ^ 2 + 7x-2} {x ^ 3 + 4x ^ 2 + 4x}$

Answer 2

2x^3 + 2x^2 + 5x + 1/ x^2