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How do you solve $\frac{2}{x + 1} = \frac{3 x}{4}$ $2/(x+1)=(3x)/4$ ?

1 Answer

Mar 4, 2018

$x = - \frac{1}{2} + \frac{\sqrt{105}}{5} xxx or xxx x = - \frac{1}{2} - \frac{\sqrt{105}}{6}$ $x=-1/2+sqrt(105)/5color(white)("xxx")"or"color(white)("xxx")x=-1/2-sqrt(105)/6$

Explanation:

Given
$XXX \frac{2}{x + 1} = \frac{3 x}{4}$ $color(white)("XXX")2/(x+1)=(3x)/4$

$\Rightarrow$ $rArr$
$XXX 2 \times 4 = (3 x) \times (x + 1)$ $color(white)("XXX")2xx4=(3x) xx (x+1)$

$XXX 8 = 3 x^{2} + 3 x$ $color(white)("XXX")8=3x^2+3x$

$XXX 3 x^{2} + 3 x - 8 = 0$ $color(white)("XXX")3x^2+3x-8=0$

(applying the quadratic formula)
$XXX x = \frac{- 3 \pm \sqrt{3^{2} - 4 \cdot 3 \cdot (- 8)}}{2 \cdot 3}$ $color(white)("XXX")x=(-3+-sqrt(3^2-4 * 3 * (-8)))/(2 * 3)$

$XXXx = \frac{- 3 \pm \sqrt{9 + 96}}{6}$ $color(white)("XXXx")=(-3+-sqrt(9+96))/6$

$XXXx = - \frac{1}{2} \pm \frac{\sqrt{105}}{6}$ $color(white)("XXXx")=-1/2+-sqrt(105)/6$

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