Find the expression. ((x^2 +2x+8)/(x^2 +2x+3.))


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Question Number 12552 by @ANTARES_VY last updated on 25/Apr/17

$Find the expression .$ $\frac{x^{2} + 2 x + 8}{x^{2} + 2 x + 3 .}$
	Answered by ajfour last updated on 25/Apr/17

	$i f y o u m e a n t h e r a n g e t h e n$ $y = \frac{x^{2} + 2 x + 8}{x^{2} + 2 x + 3} = 1 + \frac{5}{{(x + 1)}^{2} + 2}$ $y_{m a x} = 1 + \frac{5}{2} = \frac{7}{2} w h e n (x + 1) = 0$ $y_{m i n} \to 1 w h e n x \to \infty$ $s o t h e r a n g e o f t h e e x p r e s s i o n i s$ $y \in (1, \frac{7}{2}] .$
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