SOLUTION: (3x+5)/(x+5)-(x+1)/(2-x)-(4x^2-3x-1)/(x^2+3x-10)

Question 975361: (3x+5)/(x+5)-(x+1)/(2-x)-(4x^2-3x-1)/(x^2+3x-10)

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
(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)

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