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<h1>Solución</h1>
<p class="apar">Paso 1. </p>
<p>${{\sqrt {x + 2}  - 1} \over {x + 1}}$ es de la forma $0/0$ en el punto $1$.
Operando
$$\mathop {\lim }\limits_{x \to 1} {{{1 \over {x + 1}} - {1 \over 2}} \over {x - 1}} = \mathop {\lim }\limits_{x \to 1} {{{{2 - \left( {x + 1} \right)} \over {2\left( {x + 1} \right)}}} \over {x - 1}} = \mathop {\lim }\limits_{x \to 1} {{1 - x} \over {2\left( {x - 1} \right)\left( {x + 1} \right)}}$$
<p class="apar">Paso 2. </p>
<p>Simplificando
$$ = \mathop {\lim }\limits_{x \to 1} {{ - 1} \over {2\left( {x + 1} \right)}}$$
<p class="apar">Paso 3. </p>
<p>Aplicando finalmente las propiedades de los límites</p>
$$\mathop {\lim }\limits_{x \to 1} {{ - 1} \over {2\left( {x + 1} \right)}} =  - {1 \over 4}$$
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