SOLUTION: Show that, if x is real, the values of the expression {{{(x^2-3x+1)/(2x^2-3x+2)}}} can only lie between -1 and 5/7.

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Question 1041377: Show that, if x is real, the values of the expression can only lie between -1 and 5/7.
Found 2 solutions by Edwin McCravy, robertb:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Let y = the expression



Show that the denominator is never 0.

Show that it has derivative



Set that = 0 and show that it has relative 
and absolute max at (-1,5/7) and an absolute
minimum at (1,-1).

Edwin


Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
The domain of the expression is the set of all real numbers. (The discriminant of the denominator implies that it itself is never zero.)
Let .
==> (after multiplication; note that the denominator is never zero)
==> <==> .
For x to have real values, the discriminant of this equation (with x as variable) must be greater than or equal to 0.
==> <==> , or
,
<==>
The inequality is only true when y ∈ [-1, 5/7].


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