So in class i'm learning to add and subtract rational expressions how do I simplify once It's been factored out?! Can someone please explain, heres ex.

6 3x 1
____ + ___ - _______
x-6 x+5 (x-6)(x+5)

or [(6)/(x-6)]+[(3x)/(x+5])-[(1)/(x-6)(x-5)]

Options:
A. (3x+5)/(x^2-x-30)
B. (3x^2-12x+29)/(x^2-x-30)
C. (3x^2+6x+5)/(x^2-x-30)
D. (3x^2+5)/(x-6)

Question

So in class i'm learning to add and subtract rational expressions how do I simplify once It's been factored out?! Can someone please explain, heres ex. 

  6         3x            1
____  +  ___   -  _______          
x-6      x+5    (x-6)(x+5)

or [(6)/(x-6)]+[(3x)/(x+5])-[(1)/(x-6)(x-5)]

Options: 
A. (3x+5)/(x^2-x-30) 
B. (3x^2-12x+29)/(x^2-x-30) 
C. (3x^2+6x+5)/(x^2-x-30) 
D. (3x^2+5)/(x-6)

anonymous · Answer

First of all you must make sure the denominator (the number under the line) are all equal

anonymous · Answer

$$\frac{ 6\color{red}{(x+5)} }{ (x-6)\color {red}{(x+5)} }+\frac{ (3x)\color{red}{(x-6)} }{ (x+5)\color{red}{(x-6)} }-\frac{ 1 }{ (x-6)(x+5) }$$

anonymous · Answer

like that

anonymous · Answer

Now do i distribute the terms and then simplify or cancel them out?

anonymous · Answer

best to first combine them all in a single fraction

anonymous · Answer

and then distribute

anonymous · Answer

Shoot I mean 3x^2+12x+29/x^2-x-30 ? Is that correct?

anonymous · Answer

-12x, the rest is correct

anonymous · Answer

Awesome thanks!! :D I'll remember those steps!! kinda got out of order