Question

The ratio of 3 more than a number to the square of 1 more than that number is less than 1. Find the numbers which satisfy this statement.

Answer 1

How do I set this up?

Answer 2

let the number be \(a\) then \[\frac{3+a}{(a+1)^2}<1\]

Answer 3

I see now. I have been on this homework for too long. Thanks!

Answer 4

\[3+a<a^2+2a+1\]

\[a^2+a-2=(a+2)(a-1)>0\]
s0 \[a>1,a<-2\]

Answer 5

There are two "critical numbers" here. One is the value of ' a ' for which the denominator is zero. The other is the value of ' a ' for which the numerator is zero. What are these two "critical numbers?)?

Answer 6

It looks like -1 and -3

Answer 7

I agree.
Draw a number line and mark -1 and -3 on that line. These two critical values will divide your number line into 3 intervals.

Would you please identify these intervals.

Answer 8

I trust you know you can copy my graph and add to it.