Question

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

Answer 1

@radar @sammixboo @MrNood @puppylife101

Answer 2

@Yungwisdom2000 @Compassionate

Answer 3

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

Answer 4

ok thanks :)

Answer 5

\[\frac{3x+10}{ x+1} + \frac{ x+3}{x+4} - \frac{6x+27}{(x+1)(x+4)}\] Is that the right thing?

Answer 6

correct

Answer 7

It's a bit scary looking. :) Any thoughts on what you might do first?

Answer 8

we need a common denominator right :)

Answer 9

That would be REALLY nice. Yes, let's try that.

Answer 10

What might be the common denominator we are trying to make?

Answer 11

(x+1) (x+4) right

Answer 12

Seems like a good choice. That appears to be the most complicated thing in our expression. So far, so good.

Answer 13

So, let's look at the first fraction. What needs to be done here?

Answer 14

3x+10 (x+4) / x+1 (x+4) + (x+3) (x+1) / (x+4)(x+4) right

Answer 15

Yes, on the second fraction you mean (x + 1) on the bottom, but I get it. :)

Answer 16

Great! So here's what we have so far.

Answer 17

\[\frac{(3x+10) (x + 4)}{(x+1) (x + 4)}+\frac{(x+3)(x+1)}{(x+1)(x+4)}−\frac{6x+27}{(x+1)(x+4)}\]

Answer 18

Wow, that's a lot of stuff. Now what?

Answer 19

cancel out

Answer 20

Well, if we "cancel out" that might put us right back where we started right? Unless you mean distribute...

Answer 21

i'm sorry i meant distribute lol

Answer 22

No worries. :) Let's try to do that. What do you get. (Might take a minute) :)

Answer 23

im kinda lost can you draw it out

Answer 24

from where we left off

Answer 25

Sure! I think we were here right?
\[\frac{(3x+10)(x+4)}{(x+1)(x+4)}+\frac{(x+3)(x+1)}{(x+1)(x+4)}−\frac{6x+27}{(x+1)(x+4)}\]

Answer 26

yes ok, so we distribute

Answer 27

Yes, and what do you get after that?

Answer 28

i got 4/ (x+1) (x+4)

Answer 29

4 for which fraction?

Answer 30

As the final answer?

Answer 31

yes the final

Answer 32

i think i did something wrong

Answer 33

Oh, ok, let me double check that. :)

Answer 34

yes please check

Answer 35

So, for the first fraction:
\[\frac{(3x+10)(x+4)}{(x+1)(x+4)}=\frac{3x^2 + 12x + 10 x + 40}{(x+1)(x+4)}\]

Answer 36

For the second fraction:
\[\frac{(x+3)(x+1)}{(x+1)(x+4)} = \frac{x^2 + 3x + x + 3}{(x+1)(x+4)}\]

Answer 37

For the third fraction (watch out for the tricky - sign!):
\[-\frac{6x+27}{(x+1)(x+4)}=\frac{-6x-27}{(x+1)(x+4)}\]

Answer 38

ok i got 1/ (x+4)(x+1) for final

Answer 39

Checking again... :)

Answer 40

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. :)

Answer 41

ok i see, now you factor

Answer 42

hey do you mind checking this one for me

Answer 43

x/3 div 2/x+5

Answer 44

i got X(x+5) /6