anonymous
  • anonymous
can some one help me add these rational expressions?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Ok
anonymous
  • anonymous
|dw:1356272011895:dw|
anonymous
  • anonymous
Find a common denominator

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anonymous
  • anonymous
x^2+6?
anonymous
  • anonymous
I think you need to either review the distributive property or learn FOIL method
anonymous
  • anonymous
\[\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\] use \(a=8,b=x+2,c=4,d=x+3\)
anonymous
  • anonymous
use parentheses and make a direct substitution
anonymous
  • anonymous
wait so i cross multiply?
anonymous
  • anonymous
there is no such thing as "cross multiply" to add fractions, you compute \[\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}\] that is how it is always done in this case \(a=8\) so replace \(a\) by \(8\) \(b=x+2\) so replace \(b\) by \(x+2\) \(c=4\) replace \(c\) by \(4\) and \(d=x+3\) replace \(d\) by \(x+3\)
anonymous
  • anonymous
\[\frac{\overbrace{8}^a\times \overbrace{(x+3)}^d+\overbrace{(x+2)}^b\times \overbrace{4}^c}{\overbrace{(x+2)}^b\times \overbrace{(x+3)}^d}\]
anonymous
  • anonymous
do i combine the denominators?
anonymous
  • anonymous
you have a choice, you can either leave it in factored form as \[(x+2)(x+3)\] or you can multiply out using the distributive law \[(x+2)(x+3)=x^2+2x+3x+6=x^2+5x+6\] your choice
anonymous
  • anonymous
your real job is to use the distributive property in the numerator, and then combine like terms, because no one want to look at \[8(x+3)+4(x+2)\]
anonymous
  • anonymous
well to get a final answer i would need to use \[x ^{2}5x+6\] wouldnt I?
anonymous
  • anonymous
so 8x+24 + 4x+8 = 12x+32 ?
anonymous
  • anonymous
your numerator is correct, i would be \(12x+3 2\)
anonymous
  • anonymous
and your denominator is \(x^2+5x+6\)
anonymous
  • anonymous
would i have any restrictions?
anonymous
  • anonymous
yes, the same restrictions you had to begin with the denominator cannot be zero, so you know \(x\neq -2\) and also \(x\neq -3\)
anonymous
  • anonymous
so it cant be the 2 and 3 from the original denominators?
anonymous
  • anonymous
it cannot be \(-2\)
anonymous
  • anonymous
one denominator is \(x+2\) so if \(x=-2\) then you get \(-2+2=0\) and the denominator cannot be 0
anonymous
  • anonymous
ok that makes sense thanks :)
anonymous
  • anonymous
yw

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