How do you apply least common denominator when using factors with "x", like [7/x^2 + 2x-15] + [x/x^2-x-30] - [ x/x^2-9x+18 ]

Question

phi · Answer

It helps to factor the quadratics

anonymous · Answer

I know i have to factor but, i mean what then the common factors are, (x+5)(x-3)(x-6)

anonymous · Answer

What then if the common factors are*

phi · Answer

all of them multiplied together.
in each fraction, multiply top and bottom by whatever makes the bottom equal to the product of all three 
(x+5)(x-3)(x-6)

anonymous · Answer

Oh, let me try that

anonymous · Answer

So the first temr should be [7*(x+5)(x-3)(x-6)/(x+5)(x-3)* (x+5)(x-3)(x-6) ] ?

phi · Answer

that is overkill,  you want the bottom to be
(x+5)(x-3)(x-6)

you already have (x+5)(x-3)
so multiply  by (x-6)/(x-6)
this will give the common denominator

anonymous · Answer

I think I get it thanks :D

anonymous · Answer

Really thank you you saved my life today Haha.

phi · Answer

what do you get for the answer?

anonymous · Answer

[-x-42/(x+5)(x-3)(x-6)]

phi · Answer

yes, that looks good

anonymous · Answer

Yeii, thanks men. Really appreciate you quick respond