Question

(6/x^2+5x+6) + (9/x+3)

express answer in reduced form

What i attempted is to factor out the bottom half of the first fraction to

6/(x+2)(x+3)

the second half i'm guessing would be to multiply each side by the x+3? making it a (6x+18/(x+2)(x+3)) + 9

or would i write it as 6(x+3)/(x+2)(x+3) so i can cancel out the x+3 to get
6/(x+2) + 9

Answer 1

you were right to factor it, but your second part is totally bogus

I also think you placed brackets in the wrong place, probably should have been:

6/(x^2+5x+6) + 9/(x+3)
= 6/( (x+2)(x+3) ) + 9/(x+3)
we now need a common denominator which is (x+2)(x+3)
= 6/((x+2)(x+3)) + 9(x+2)/( (x+2)(x+3) )
= ( 6 + 9x + 18)/( (x+2)(x+3) )
= (9x + 24)/( (x+2)(x+3) )
=<b> 3(3x + 8)/( (x+2)(x+3) )</B>

I usually test my answer by picking any value of x in the original and in the answer.
let x = 0
in original: 6/(0+0+6) + 9/(0+3)
=6/6 + 9/3 = 1+3 = 4
my answer:
3(0+8)/( (2)(3) )
= 24/6 = 4

There is a very high probability that my answer is correct