Show that for all real values of x, ((x^2)+2x+1)/(x+1) does not lie between -3 and 1.

Question

This question is under algebra section .

Answer 1

The numerator can be written (x+1)^2, so the expression reduces to x+1 as long as x≠-1.

But this value of x is the only prohibited value, so it is not true that the expression does not lie between -3 and 1. For example, when x=-2, the expression has a value of -1 which lies between -3 and 1.