anonymous
  • anonymous
Perform the following operations and prove closure. x/x+3 + x+2/x+5
Mathematics
chestercat
  • chestercat
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anonymous
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anonymous
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anonymous
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anonymous
  • anonymous
|dw:1436973914482:dw|
anonymous
  • anonymous
commond denominator (x+3)(x+5) |dw:1436974232640:dw|
anonymous
  • anonymous
|dw:1436974357719:dw|
anonymous
  • anonymous
Yes, yes I see :)
anonymous
  • anonymous
2x^2+10x+6/(x+3)(x+5
anonymous
  • anonymous
yes?
anonymous
  • anonymous
yes. and you can combine the denominator to x²+8x+15
anonymous
  • anonymous
How do I do that?
anonymous
  • anonymous
|dw:1436974690367:dw| then the final result is \[\frac{ 2x^2+10x+6 }{ x^2+8x+15 }\]
anonymous
  • anonymous
:) Thanks!!!
anonymous
  • anonymous
And the closure would be -3,5
anonymous
  • anonymous
-3 and -5
anonymous
  • anonymous
oh :)
anonymous
  • anonymous
Can I ask another?
anonymous
  • anonymous
x plus 4 over x squared plus 5x plus 6 times x plus 3 over x squared minus 16.
anonymous
  • anonymous
this? \[\frac{ x+4 }{ x^2+5x+6 } \times \frac{ 3 }{ x^2-16 }\]
anonymous
  • anonymous
|dw:1436975237198:dw|
anonymous
  • anonymous
Yeah
anonymous
  • anonymous
ok. you can factor the denominators and then cancel to make the multiplication easier. do you know how?
anonymous
  • anonymous
Yes x2+5x+6 = (x+2)(x+3)
anonymous
  • anonymous
yes, and you can factor x²-16 too
anonymous
  • anonymous
(x-4)(x+4)
anonymous
  • anonymous
right, so now it's this and you can cancel |dw:1436975608076:dw|
anonymous
  • anonymous
so 1/x+2(x-4)
anonymous
  • anonymous
closure would be -2,4
anonymous
  • anonymous
yes that's right

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