anonymous
  • anonymous
Adding Rational Expressions
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ 2x+6 }{ (x+3)^2 } + \frac{ x }{ x+3 }\]
skullpatrol
  • skullpatrol
Any ideas?
anonymous
  • anonymous
I started by multiplying the denominator and numerator by (x + 3) on the second fraction so that it would have the same denominator...

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anonymous
  • anonymous
|dw:1378586720615:dw|
anonymous
  • anonymous
Is that right so far :L
anonymous
  • anonymous
Also I simplified (x + 3)^2 to x^2 + 9 but I don't know if I was suppose to do that...
anonymous
  • anonymous
\[\frac{a}{b^2}+\frac{c}{b}=\frac{a}{b^2}+\frac{c b}{b^2}=\frac{a+c b}{b^2} \]
anonymous
  • anonymous
I know that much but if I did that I would have: \[\frac{ 2x+6 }{ x^2+9 } + \frac{ x(x+3) }{ x^2+9 }\]
anonymous
  • anonymous
Now I don't really know what parts to add...
anonymous
  • anonymous
The above is correct. Now add the numerators together.
skullpatrol
  • skullpatrol
Write it all over the common denominator.
anonymous
  • anonymous
should I simplify x(x+3) to x^2+3x?
anonymous
  • anonymous
Take over @skullpatrol. I just spent 10 days in purgatory for "providing answers".
anonymous
  • anonymous
\[\frac{ 2x+6 }{ x^2+9 } + \frac{ x^2 + 3x }{ x^2+9 } = \frac{ x^2 +5x + 6 }{ x^2 + 9 }\]
anonymous
  • anonymous
Is that ok?
skullpatrol
  • skullpatrol
Yes.
anonymous
  • anonymous
Would I have to factor it further?
skullpatrol
  • skullpatrol
Go ahead and try :-)
anonymous
  • anonymous
\[\frac{ (x+3)(x+2) }{ (x+3)(x+3) }\] and then I guess the x+3's would cancel out leaving: \[\frac{ x+2 }{ x+3 }\]
anonymous
  • anonymous
\[\frac{ (x+3)(x+2) }{ (x+3)(x+3) }\] and then I guess the x+3's would cancel out leaving: \[\frac{ x+2 }{ x+3 }\]
skullpatrol
  • skullpatrol
Are you sure that the denominator factors that way?
anonymous
  • anonymous
Yea because if you multiply x+3 by x+3 you would get x^2 + 9
skullpatrol
  • skullpatrol
Use FOIL to prove it please.
anonymous
  • anonymous
|dw:1378587703476:dw|
anonymous
  • anonymous
:(
skullpatrol
  • skullpatrol
So you learned something...
anonymous
  • anonymous
SO what would the factor be then?
anonymous
  • anonymous
I still think that its (x+3)(x+3) because since the it doesn't have the "bx" in ax^2+bx+c shouldn't we just ignore it?
anonymous
  • anonymous
Cause tis not a trinomial
skullpatrol
  • skullpatrol
You can not just "ignore" the middle term you PROVED with FOIL, right?
anonymous
  • anonymous
So then what would it be for x^2 + 9
anonymous
  • anonymous
This is how I see it:|dw:1378588338974:dw|
skullpatrol
  • skullpatrol
What about the "OI" in FOIL?
anonymous
  • anonymous
Maybe there's an exception :L
skullpatrol
  • skullpatrol
Where would you look to find the exception to any rule in math?
anonymous
  • anonymous
A black hole :)|dw:1378588587370:dw| No but seriously if it's not (x+3)(x+3) then what is it?
skullpatrol
  • skullpatrol
$$\Huge x^2+3^2$$does not factor.
anonymous
  • anonymous
So it would just be left like that? without any further simplifying?
skullpatrol
  • skullpatrol
Yes.

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