Help solve please medal! Simplify 3x+10/ x+1 + x+3/x+4 -6x+27/(x+1)(x+4)

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Help solve please medal! Simplify 3x+10/ x+1 + x+3/x+4 -6x+27/(x+1)(x+4)

Mathematics
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I'm going to rewrite this to make sure we are looking at the same thing. :)

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ok thanks :)
\[\frac{3x+10}{ x+1} + \frac{ x+3}{x+4} - \frac{6x+27}{(x+1)(x+4)}\] Is that the right thing?
correct
It's a bit scary looking. :) Any thoughts on what you might do first?
we need a common denominator right :)
That would be REALLY nice. Yes, let's try that.
What might be the common denominator we are trying to make?
(x+1) (x+4) right
Seems like a good choice. That appears to be the most complicated thing in our expression. So far, so good.
So, let's look at the first fraction. What needs to be done here?
3x+10 (x+4) / x+1 (x+4) + (x+3) (x+1) / (x+4)(x+4) right
Yes, on the second fraction you mean (x + 1) on the bottom, but I get it. :)
Great! So here's what we have so far.
\[\frac{(3x+10) (x + 4)}{(x+1) (x + 4)}+\frac{(x+3)(x+1)}{(x+1)(x+4)}−\frac{6x+27}{(x+1)(x+4)}\]
Wow, that's a lot of stuff. Now what?
cancel out
Well, if we "cancel out" that might put us right back where we started right? Unless you mean distribute...
i'm sorry i meant distribute lol
No worries. :) Let's try to do that. What do you get. (Might take a minute) :)
im kinda lost can you draw it out
from where we left off
Sure! I think we were here right? \[\frac{(3x+10)(x+4)}{(x+1)(x+4)}+\frac{(x+3)(x+1)}{(x+1)(x+4)}−\frac{6x+27}{(x+1)(x+4)}\]
yes ok, so we distribute
Yes, and what do you get after that?
i got 4/ (x+1) (x+4)
4 for which fraction?
As the final answer?
yes the final
i think i did something wrong
Oh, ok, let me double check that. :)
yes please check
So, for the first fraction: \[\frac{(3x+10)(x+4)}{(x+1)(x+4)}=\frac{3x^2 + 12x + 10 x + 40}{(x+1)(x+4)}\]
For the second fraction: \[\frac{(x+3)(x+1)}{(x+1)(x+4)} = \frac{x^2 + 3x + x + 3}{(x+1)(x+4)}\]
For the third fraction (watch out for the tricky - sign!): \[-\frac{6x+27}{(x+1)(x+4)}=\frac{-6x-27}{(x+1)(x+4)}\]
ok i got 1/ (x+4)(x+1) for final
Checking again... :)
I get: (3x^2 + x^2 + 22x + 4x - 6x + 40 + 3 - 27)/(x+1)(x+4) so (4x^2 + 20x + 16)/(x+1)(x+4) so (2x + 2)(2x + 8)/(x+1)(x+4) then 2(x+1)*2(x+4)/(x+1)(x+4) Oh wow! 4 is the final answer. I think. :)
ok i see, now you factor
hey do you mind checking this one for me
x/3 div 2/x+5
i got X(x+5) /6

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