Can someone help me simplify the following?

Question

x-2

---------------

x^2+3x+2

minus

x-1

---------

x^2-4

Answer 1

x-2 / x^2 + 3x + 2  - x-1 / x^2 - 4

in the denominator, the right side needs a (x-2) and the right needs an (x+1).  multiply the numerators by those and you have a common denominator (ill call it function f(x)  )

(x-2)(x-2) / f(x)  - (x-1)(x+1) / f(x)

(x^2 - 4x + 4) / f(x) - ((x^2 - 2x +1) / f(x) )

subtract numerators

-2x-3 / (x+2)(x+1)(x-2)

there might be a simpler way, double check other answers  

Answer 2

First make the denominators equal

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

(x+2) are common factors

Now combine and subtract

((x-2)(x-2)/(x+2)(x-2)(x+1))-((x-1)(x+...

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

factor the denominator out and get x^3+1x^2-4x-4

(-4x+5)/x^3+1x^2-4x-4