Question

find the domain of y=sqrt[(x+4)/(x-5)]

Answer 1

so (x+4)/(x-5)>=0 --> (x+4)*(x-5)>=0
can you do it now?

Answer 2

how did you achieve that?

Answer 3

do you know anything in a square root has to be greater or equal to 0?

Answer 4

yes

Answer 5

how did the divide sign change into a multiply sign?

Answer 6

now, as you do not know if (x-5) is positive or negative, you cant take it to the other side. if it is negative the greater sign will change to less than sign.
now, multiply both denominator and numerator by x-5. denominator becomes (x-5)^2. now this is always positive. so you can take it to the other side as (x-5)^2*0=0.
so the equation becomes (x-4)*(x-)>=0

Answer 7

(x-5)* in the last line.

Answer 8

i get it now,
so if you draw a graph,
x<-4 and x>5

Answer 9

thats right. dont forget the equal to sign.

Answer 10

thanks

Answer 11

you're welcome.