Question

Subtract and simplify answer.
3x/x^2+4x+3 - x-6/x+1

Answer 1

I got the answer -x^2-9x-18/(x+3)(x+1) .. Its wrong. -6x is the correct part not -9x... How is it -6x?

Answer 2

this?
\[\frac{ 3x }{ x^2+4x+3 }-\frac{ x-6 }{ x+1 }\]

Answer 3

Yes.

Answer 4

factor on the right and get a common denominator
\[\frac{ 3x }{ (x+3)(x+1) }-\frac{ (x-6)(x+3) }{ (x+3)(x+1) }\]
combine into one fraction
\[\frac{ 3x-((x-6)(x+3)) }{ (x+3)(x+1) }\]
foil
\[\frac{ 3x-(x^2-6x+3x-18) }{ (x+3)(x+1) }\]
distribute the negative
\[\frac{ 3x-x^2+6x-3x+18 }{ (x+3)(x+1) }\]
combine like terms
\[\frac{ -x^2+6x+18 }{ (x+3)(x+1) }\]

Answer 5

or if you factor out the negative in front of x²
\[-\frac{ x^2-6x-18 }{ (x+3)(x+1) }\]

Answer 6

Okay I see how you got 6.. But why did you put -6 before 3?

I have --- (x-6)(x+3)== (x^2+3x-6x-18)

Answer 7

addition is commutative, meaning the order doesn't matter

Answer 8

1 + 2 is the same as 2 + 1

Answer 9

Okay..

Answer 10

What your saying isnt right.. Your answer-> 3+6-3=6 Mine-->3+3-6=0
By changing where the numbers go gives a completely different number.

Answer 11

Never mind Ill wait for a response from my teacher. Thanks for I guess helping.

Answer 12

I wouldn't know what yours is, or how you got it because you haven't shown me any work.

Answer 13

All you had to do was ask..

x^2+4x+3= (x+3)(x+1)

3x/ (x+3)(x+1) - x-6/x+1 * (x+3)/(x+3)

3x-(x-6)(x+3)/ (x+3)(x+1)

3x-(x^2+3x-6x-18/ (x+3)(x+1)

--3x-6x=-3--

-x^2-9x-18/(x+3)(x+1)

Answer 14

no offense, but you're asking the question. I really shouldn't have to ask to see your work.

This is your 4th line:
3x-(x^2+3x-6x-18)/ (x+3)(x+1)

You have to distribute the - sign. It's kind of like a -1 in front of the parentheses.
3x -1(x² + 3x - 6x - 18)
3x - x² - 3x + 6x + 18

Just the x terms is 3x - 3x + 6x

so the whole numerator is
-x² + 6x + 18

Answer 15

it just looks like you didn't distribute