Question 975361
(3x+5)/(x+5)  + (x+1)/(x-2) -  [(4x^2-3x-1)/(x+5)(x-2)]

I did two things here.  I changed the sign of the second term and made the denominator (x-2)
I did not factor the numerator after the minus sign, but I did factor the denominator.  Note that I can add these if I use a common denominator of (x+5) and (x-2).  The first two terms will change, but not the last.  Then I can subtract

(3x+5) (x-2)=3x^2-x-10
(x+1)(x+5)=x^2+6x+5
These two will be the first two terms over the common denominator.

Ignoring for the moment the common denominator, we combine terms, subtracting 4x^2-3x-1, and all terms will change signs.

3x^2-x-10+x^2+6x+5-4x^2+3x+1

The x^2 cancel.
-x-10+6x+5+3x+1
This is 8x-4= 4(2x-1)

That is over the common denominator of (x+5)(x-2)



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