anonymous
  • anonymous
Simplify.. need help asap... 8/ab + 6/b and (3t2/(t + 2)) x ((t + 2)/t2) thanks!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jim_thompson5910
  • jim_thompson5910
The first one is \[\Large \frac{8}{ab} + \frac{6}{b}\] right?
anonymous
  • anonymous
yes.
jim_thompson5910
  • jim_thompson5910
what is the LCD in this case?

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More answers

anonymous
  • anonymous
i don't know.
jim_thompson5910
  • jim_thompson5910
we have ab as the first denominator and b as the second denominator
jim_thompson5910
  • jim_thompson5910
do you see how the LCD would be ab?
anonymous
  • anonymous
no.
anonymous
  • anonymous
:( I'm really bad at math. I'm sorry..
jim_thompson5910
  • jim_thompson5910
maybe replace a and b with numbers
jim_thompson5910
  • jim_thompson5910
say a = 2 b = 3
anonymous
  • anonymous
okay.
jim_thompson5910
  • jim_thompson5910
ab = 2*3 = 6
anonymous
  • anonymous
i understand that.
jim_thompson5910
  • jim_thompson5910
if we had 1/6 + 1/3, what would the LCD be?
anonymous
  • anonymous
6
jim_thompson5910
  • jim_thompson5910
yes because we can multiply the denominator 3 by 2 to get 6
jim_thompson5910
  • jim_thompson5910
we can multiply top and bottom of 1/3 by 2 to get 2/6 1/6 + 1/3 turns into 1/6 + 2/6
jim_thompson5910
  • jim_thompson5910
from there you add straight across and leave the denominator alone
anonymous
  • anonymous
mhm.
jim_thompson5910
  • jim_thompson5910
the same idea applies here we multiply top and bottom of the second fraction by 'a' \[\Large \frac{8}{ab} + \frac{6}{b}\] \[\Large \frac{8}{ab} + \frac{6{\color{red}{a}}}{b{\color{red}{a}}}\] \[\Large \frac{8}{ab} + \frac{6a}{ab}\]
jim_thompson5910
  • jim_thompson5910
then you add the numerators and place that over the denominator
anonymous
  • anonymous
okat.
anonymous
  • anonymous
now I'm lost.
jim_thompson5910
  • jim_thompson5910
where at?
anonymous
  • anonymous
how do we find the answer? or did we already find it and i was lost before then? i thought I've been following.
jim_thompson5910
  • jim_thompson5910
do you see why I multiplied top and bottom of the second fraction by 'a'?
jim_thompson5910
  • jim_thompson5910
I wanted to get every denominator equal to the LCD 'ab'
anonymous
  • anonymous
okay
jim_thompson5910
  • jim_thompson5910
there's one more step to go
anonymous
  • anonymous
alright.
jim_thompson5910
  • jim_thompson5910
What does \[\Large \frac{8}{ab} + \frac{6a}{ab}\] simplify to?
anonymous
  • anonymous
8/ab + 6/ab
anonymous
  • anonymous
i really am lost.
anonymous
  • anonymous
8/ab+6/b
jim_thompson5910
  • jim_thompson5910
just add up the numerators \[\Large \frac{8}{ab} + \frac{6a}{ab}=\frac{8+6a}{ab}\] this is possible because the denominators are both equal to ab
anonymous
  • anonymous
okay. now how would we do the second one?
jim_thompson5910
  • jim_thompson5910
The second one is \[\Large \left(\frac{3t^2}{t+2}\right)\times\left(\frac{t+2}{t^2}\right)\] right?
anonymous
  • anonymous
t+2 on the sec on one are in a parenthesis.
anonymous
  • anonymous
and in the first one. its like parenthesis insides of themselves.
jim_thompson5910
  • jim_thompson5910
ok so this? \[\Large \left(\frac{3t^2}{(t+2)}\right)\times\left(\frac{(t+2)}{t^2}\right)\]
anonymous
  • anonymous
yes that is correct.
jim_thompson5910
  • jim_thompson5910
first notice this cancellation \[\Large \left(\frac{3{\color{red}{\cancel{\color{black}{t^2}}}}}{t+2}\right)\times\left(\frac{t+2}{{\color{red}{\cancel{\color{black}{t^2}}}}}\right)\] the t^2 terms will go away leaving just \[\Large \left(\frac{3}{(t+2)}\right)\times\left(\frac{(t+2)}{1}\right)\]
anonymous
  • anonymous
ok what is the next step
jim_thompson5910
  • jim_thompson5910
then the (t+2) terms also cancel \[\Large \left(\frac{3}{{\color{red}{\cancel{\color{black}{(t+2)}}}}}\right)\times\left(\frac{{\color{red}{\cancel{\color{black}{(t+2)}}}}}{1}\right)\]
jim_thompson5910
  • jim_thompson5910
I'm sure you see how to finish
anonymous
  • anonymous
so its 3?
jim_thompson5910
  • jim_thompson5910
yep
anonymous
  • anonymous
thats the easiest thing I've ever seen

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