Question

Divide:
1)2x+2/x^2+5x+6 / x^2+4x+3
2)x^2+2x-15/x-3 / x+5/6x-18

Answer 1

\[1) \frac{ 2x+2 }{x^{2}+5x+6 } \div x^{2}+4x+3\]

Answer 2

2)\[\frac{ x^{2}+2x-15 }{ x-3 } \div /\frac{x+5}{6x-18}\]

Answer 3

@hartnn

Answer 4

ok, try to factor whichever expression you can. go one by one
2x+2 =... ? (this is easy)
x^2+5x+6 =... ?

Answer 5

1) 1

Answer 6

(x+3)(x+2)

Answer 7

2x+2 = 1 ?? :O

Answer 8

x^2+5x+6 = (x+3)(x+2) is correct :)

Answer 9

Oh I thought it was 2x+2=0 haha

Answer 10

2x+2 = 2 (x+1)
got this ?
x^2+4x+3 =... ?

Answer 11

OH my mistake. So then the bottom would be ...x+2 x+1 .. No ..

Answer 12

hmm .. ?
ok, one by one
2x+2 = 2 (x+1)
x^2+5x+6 = (x+3)(x+2) is correct.
what about x^2+4x+3 =... ?

Answer 13

we'll see tops and bottoms later... :P

Answer 14

that would be .. (x+1)(x+3) Ah no , the last line I'm stuck on factoring o;

Answer 15

yes,
thats correct.

Answer 16

Oh okay yay lol.

Answer 17

\[\frac{ 2(x+1) }{(x+3)(x+2) } \div (x+1)(x+3)\]

Answer 18

\(\large \dfrac{ 2(x+1) }{(x+3)(x+2) } \div (x+1)(x+3)=\dfrac{ 2(x+1) }{(x+3)(x+2) } \times \dfrac{1}{ (x+1)(x+3)}\)
what gets cancelled ?

Answer 19

also, you got that step ?

Answer 20

2 / (x+2) = 1

Answer 21

:O
first just tell me what gets cancelled ?

Answer 22

x+1, x+3

Answer 23

sure, does 'x+3' really get cancelled ? and yes, x+1 gets cancelled.

Answer 24

Oh no it doesn't. So then we're left with.. 2/x+3 x+2 = 1/x+3

Answer 25

how is the numerator = 1 ?

Answer 26

Oh no no , it's just what's on the other side.

Answer 27

Oh I meant x

Answer 28

\(\large \dfrac{ 2\cancel{(x+1)} }{(x+3)(x+2) } \times \dfrac{1}{ \cancel{(x+1)}( {x+3})}=\dfrac{2}{(x+2)(x+3)^2}\)
is what remas and cannot be simplified, so the answer...

Answer 29

Thank you so much again! I understand it so much better. One last problem? So sorry for wearing you out!

Answer 30

The second equation now D: Haha . :) Then I'm done.

Answer 31

no problem :)
6x-18 =... ?

Answer 32

x^2+2x-15 =... ?

Answer 33

umm...(x+6)(x-3) for what ?
6x-18 = 6 (......?.....)

Answer 34

6(x+3)

Answer 35

6 (x+3) or 6 (x-3) ??

Answer 36

Ooh x-3 xD

Answer 37

x^2+2x-15 =... ?

Answer 38

Um.. I'm not sure? D:

Answer 39

Oh wait.

Answer 40

(x+5)(x-3)?

Answer 41

yes!

Answer 42

Yay.

Answer 43

what gets cancelled ?

Answer 44

x-3

Answer 45

x+5

Answer 46

yes :) what remains ?

Answer 47

6(x-3) ?

Answer 48

Oh wait. x-3 / 6(x-3)

Answer 49

\(\large \frac{ x^{2}+2x-15 }{ x-3 } \div \frac{x+5}{6x-18} \\ = \large \frac{ x^{2}+2x-15 }{ x-3 } \times \frac{6x-18}{x+5} = \dfrac{\cancel{(x+5)}\cancel{(x-3)}}{\cancel{x-3}} \dfrac{6(x-3)}{\cancel{x+5}}\)
what remains ?

Answer 50

Just 6(x-3) ? Like i originally thought lol. That's the final answer?

Answer 51

yes! :P

Answer 52

Thank you so very much @hartnn ! :) Have a good night xo

Answer 53

I appreciate it!

Answer 54

well, you have an awesome night , and sweet dreams ^_^
its morning here, i'll start my day :)