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moongazer Group TitleBest ResponseYou've already chosen the best response.1
how do you find it? stepbystep please :)
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
√(x^2  9x +20)/√(x^2  5x + 6) I already know the domain. But, how do you get it?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
first workout contraints for squareroot : the thing inside squareroot cannot be negative
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
next work out constraints for denominator : denominator cannot be equal to 0
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
consider numerator first : \(\sqrt{x^2  9x +20}\)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
can u work out domain for that ?
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
{xx>=5} is that right?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
somewhat right :) lets see how to solve
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
x^29x+20 >= 0 x^24x5x+20 >=0 x(x4) 5(x4) >= 0 (x4)(x5) >= 0 x <= 4 or x >= 5
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
thats one constraint for numerator, lets find out the constraints for denominator
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
I think I am starting to understand it :)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
good :) since, denominator is also under radical, it must be >=0 : x^2  5x + 6 >= 0 x^23x2x + 6 >= 0 x(x3) 2(x3) >= 0 (x2)(x3) >= 0 x <= 2 or x >= 3
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
with those two things, we finished with the first step of finding constraints for radicals
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
so far we have this : x <= 4 or x >= 5 x <= 2 or x >= 3
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
yup, I understand it :)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
next one is denominator can never equal to 0. so, x^2  5x + 6 \(\ne\) 0 x^23x2x + 6 \(\ne\) 0 x(x3) 2(x3) \(\ne\) 0 (x2)(x3) \(\ne\) 0 x \(\ne\) 2 or x \(\ne\) 3
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
w8 Isn't it that it should be: x >= 4 or x >= 5 x >= 2 or x >= 3 ???
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
lets combine all constraints and make a meaningful constraint
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
which one ?
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
(x4)(x5) >= 0 (x2)(x3) >= 0
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
oh i got ur question, il give quick explanation
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
you comfortable with parabola graph ?
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
I think so
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
il show u in graph why its x <=4 , x >=5
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
I know few things about parabola
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
im sketching this parabola : (x4)(x5) >= 0
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
it intersect x axis at 4, 5 right ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
dw:1348496600444:dw
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
between 4 and 5, it is sinking down into x axis eh ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
its becoming NEGATIVE
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
dw:1348496705657:dw
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
why did it intersect in x axis at 4, 5?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
when u factored you got : (x4)(x5)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
that means it intersects xaxis at 4 and 5
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
ohh, ok what if it says (x4)(x+5) does it intersect at 4 and 5 ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
thats right, when it says, (x4)(x+5) = 0 then it intersects at 4 and 5
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
cuz for it to equal to 0, one of both of the factors must equal to 0
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
dw:1348498226449:dw
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
so the graph is like that?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
perfect, thats (x4)(x+5)
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
and the domain is x>=4,x<=5 is it correct?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
thats right ! you became expert ;p
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
for (x4)(x+5)
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
Thanks! I know understand it. :) let's now continue with our previous discussion :)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
great ! so far what we have
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
next one is denominator can never equal to 0. so, x^2  5x + 6 ≠ 0 x^23x2x + 6 ≠ 0 x(x3) 2(x3) ≠ 0 (x2)(x3) ≠ 0 x ≠ 2 or x ≠ 3
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
yeah we almost done
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
lets put down all the 3 constraints we got in one place :
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
1) numerator radical : x <= 4 or x >= 5 2) denominator radical : x <= 2 or x >= 3 3) denominator cant be 0 : x ≠ 2 or x ≠ 3
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
I understand it. What's next?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
see 2) and 3)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
can we combine them as one, like this : 2) 3) : x < 2 or x > 3
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
I'll be back just continue.
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
someone is calling me
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
ok after combining 2) and 3) we are left with : 1) numerator radical : x <= 4 or x >= 5 2) x < 2 or x > 3 this is the last step. see if u can figure out
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
out of x < 2 & x <= 4, x < 2 is more restrictive, so we have this in our domain : \(\color{green}{x < 2}\)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
out of x > 3 & x <= 4 x > 3 , x <= 4 , which is same as : \(\color{green}{3<x\le 4}\)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
and of course the last one, \(\color{green}{x >= 5}\)
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
sorry for being away, I'm here again :)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
np :) see if above stuff makes sense
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
it makes sense but why in the final answer they used "or" not "and" "," "then" or anything else dom K: {xx<2 or 3<x<=4 or x>=5}
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
yeah we always combine domain with "or" why ? cuz its meaningful. let me ask u a q
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
suppose we write : x < 2 and x >=5
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
for the domain it is ALWAYS "or" ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
is that possible ? can x be BOTH less than 2 and greater than 5 at the SAME time ha ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
yes always "or"
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
yes, it is not possible
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
is "1" less than 2 and greater than "5" ?
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
yeah, but if we put it like this : either "1" is less than 2 or greater than "5"
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
how meaningful it is, so while phrasing domain also, we use commonsense aswell :)
 2 years ago

moongazer Group TitleBest ResponseYou've already chosen the best response.1
yes, Thank you very much for helping me :)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
np i learned as well. i forgot these long back in college... i enjoyed going thru these again.. thnks you too :)
 2 years ago
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