Question

Please answer this question showing your solving step-by-step

The answers are -2/3 and 1

Only answer question 18)

Answer 1

Solution :

$\dfrac{2}{x}\: + \: \dfrac{2}{x\: + \: 1}\: = \: 3$

$\dfrac{2(x\: + \: 1)\: + \: 2(x)}{x(x+1)} \: = \: 3$

$\dfrac{2x \: + \: 2 \: + \: 2x}{x^{2} \: + \: x}\: = \: 3$

$4x \: + \: 2\: = \: 3[x^{2}\: + \: x]$

$4x \: + \: 2\: = \: 3x^{2}\: + \: 3x$

$3x^{2}\: + \: 3x \: = \: 4x \: + \: 2$

$3x^{2}\: + \: 3x\: -\: 4x \: - \: 2 \: = \:0$

$3x^{2} \: - \: x \: -\: 2 \: = \: 0$

$3x^{2} \: -\: 3x \: +\: 2x \: -\: 2\: = \: 0$

$3x(x\: - \: 1)\: +\:2(x\: -\: 1) \: = \: 0$

$(3x\: + \: 2)(x\: - \: 1)\: = \: 0$

Now,

First pair

$3x \: + \: 2 \: = \: 0$

$x \: = \: \dfrac{-2}{3}$

Second pair

$x \: - \: 1\: = \: 0$

$x \: = \: 1$

Answers

$\boxed{ x \: = \: \dfrac{-2}{3}}$

$\boxed{x \: = \: 1}$