solve: (√(((x^2 +4x+4)/(x^2 +5x+6)) )) + 2 (√((x^2 +5x+6)/(x^2 +4x+4))) =?


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Question Number 172030 by Mikenice last updated on 23/Jun/22

$s o l v e :$ $\sqrt{\frac{x^{2} + 4 x + 4}{x^{2} + 5 x + 6}} + 2 \sqrt{\frac{x^{2} + 5 x + 6}{x^{2} + 4 x + 4}} = ?$
	Answered by Rasheed.Sindhi last updated on 23/Jun/22

	$S i m p l i f y i n g (N o t s o l v i n g) :$ $\frac{\sqrt{x^{2} + 4 x + 4}}{\sqrt{x^{2} + 5 x + 6}} + \frac{2 \sqrt{x^{2} + 5 x + 6}}{\sqrt{x^{2} + 4 x + 4}}$ $= \frac{x^{2} + 4 x + 4 + 2 (x^{2} + 5 x + 6)}{\sqrt{x^{2} + 5 x + 6} \sqrt{x^{2} + 4 x + 4}}$ $= \frac{3 x^{2} + 14 x + 16}{(x + 2) \sqrt{(x + 2) (x + 3)}}$ $= \frac{(x + 2) (3 x + 8)}{(x + 2) \sqrt{(x + 2) (x + 3)}}$ $= \frac{(3 x + 8) \sqrt{(x + 2) (x + 3)}}{(x + 2) (x + 3)}$
	Commented by Mikenice last updated on 23/Jun/22

	$t h a n k s s i r$
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