Solve for x: ((√(x + 1))/x) + (√(x/(x + 1))) = ((13)/6)


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Question Number 20047 by tawa tawa last updated on 20/Aug/17

$Solve for x :$ $\frac{\sqrt{x + 1}}{x} + \sqrt{\frac{x}{x + 1}} = \frac{13}{6}$
	Answered by ajfour last updated on 21/Jun/18

	$f i r s t t e r m i s \sqrt{\frac{x + 1}{x}} o r \frac{\sqrt{x + 1}}{x} ?$ $a s s u m i n g i t i s \sqrt{\frac{1 + x}{x}};$ $l e t \sqrt{\frac{1 + x}{x}} = t$ $t h e n t + \frac{1}{t} = \frac{13}{6}$ $6 t^{2} - 13 t + 6 = 0$ $6 t^{2} - 4 t - 9 t + 6 = 0$ $2 t (3 t - 2) - 3 (3 t - 2) = 0$ $t = \frac{3}{2}, \frac{2}{3} .$ $\frac{x + 1}{x} = \frac{9}{4}, \frac{4}{9}$ $4 x + 4 = 9 x o r 9 x + 9 = 4 x$ $x = \frac{4}{5} o r x = - \frac{9}{5} .$
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