Question

explain the different types of internet connections.​

Answer 1

$\blue{\mathtt {Solution}}− \\ </p><p></p><p>Given \: inequality \:  is \: \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ {x}^{2} - \: 3x \: + \: 4}{x \: + \: 1} > 1 \\ </p><p></p><p>can \: be \: rewritten \:  as \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ {x}^{2} - \: 3x \: + \: 4}{x \: + \: 1} - 1 > 0 \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ {x}^{2} - \: 3x \: + \: 4 - \: (x + 1)}{x \: + \: 1} > 0 \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ {x}^{2} - \: 3x \: + \: 4 - \: x \: - \: 1}{x \: + \: 1} > 0 \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ {x}^{2} - \: 4x \: + \: 3 }{x \: + \: 1} > 0 \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ {x}^{2} - \: 3x - x \: + \: 3 }{x \: + \: 1} > 0 \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ x(x - 3) - 1(x - 3)}{x \: + \: 1} > 0 \\ </p><p></p><p>\rm :\longmapsto\:\dfrac{ (x - 3) (x - 1)}{x \: + \: 1} > 0 \\ </p><p></p><p>So, \:  breaking \: points \: are \: - 1, 1 \: and \: 3. \\ </p><p></p><p>So, \:  intervals \:  along \: with  \: \\ their \: respective \: signs \:  of \:  inequality \:  are \: as  \\ \: follow :- \\ </p><p></p><p>\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf Interval & \bf Sign \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf ( - \infty , - 1) & \sf - \\ \\ \sf ( - 1,1) & \sf + \\ \\ \sf (1,3) & \sf - \\ \\ \sf (3, \infty ) & \sf + \end{array}} \\ \end{gathered}\end{gathered} \\ </p><p></p><p>So, \:  Solution \: set \:  is \\ </p><p></p><p> \mathcal{\bf\implies \:\boxed { \bf \red{x \in \: ( - 1, \: 1) \: \cup \: (3, \: \infty ) \: }}}</p><p></p><p></p><p>$

Answer 2

Answer:

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