exercise with sets

[ignaziobong]

Hello, this exercise is too complex for me, can someone help me please

best regards

 

[R.M.]

I'd start by asking what value(s) of x make each fraction 0. Then move on to asking in A, what values of x make that ratio negative? For B, what values of x make the ratio positive (don't forget to consider +/+ and -/- cases). Not the most elegant approach, but the first one that popped into head.

 

[pka]

Hello, this exercise is too complex for me, can someone help me please

best regards

Please review the posted image because it means that [imath]B\subseteq A[/imath]
If that is correct then [imath]B\cap A=B[/imath]

 

[Dr.Peterson]

Hello, this exercise is too complex for me, can someone help me please

best regards

To reinforce pka's comment,

Please review the posted image because it means that [imath]B\subseteq A[/imath]
If that is correct then [imath]B\cap A=B[/imath]

all it takes to see this is to see what I've circled:

​

Now, the two rational inequalities are a little tricky to solve, because the denominators can't be factored; this observation cuts the difficulty in half, and sketching the graph of the denominator can help with the remaining hard part.

Let us know what ideas you have, and what conclusions you draw.