Question

please answer this question please dears ​

Answer 1

$\large \longrightarrow \rm \lim \limits_{ \rm x \rightarrow2} \bigg( \dfrac{1}{x - 2} - \dfrac{4}{ {x}^{3} - 2 {x}^{2} } \bigg) \\ \\ \\ \large \longrightarrow \rm \lim \limits_{ \rm x \rightarrow2} \bigg( \dfrac{1}{x - 2} - \dfrac{4}{ {x}^{2} ({x}^{} - 2)} \bigg) \\ \\ \\ \large \longrightarrow \rm \lim \limits_{ \rm x \rightarrow2} \bigg( \: \dfrac{ {x}^{2} - 4}{ {x}^{2} ({x}^{} - 2)} \: \bigg)\\ \\ \\ \large \longrightarrow \rm \lim \limits_{ \rm x \rightarrow2} \bigg( \: \dfrac{ {x}^{2} - {2}^{2} }{ {x}^{2} ({x}^{} - 2)} \: \bigg)\\ \\ \\ \large \longrightarrow \rm \lim \limits_{ \rm x \rightarrow2} \: \dfrac{ ({x}^{} - {2}^{} ) (x + 2)}{ {x}^{2} ({x}^{} - 2)} \: \\ \\ \\ \large \longrightarrow \rm \lim \limits_{ \rm x \rightarrow2} \: \dfrac{ \cancel{({x}^{} - {2}^{} }) (x + 2)}{ {x}^{2} \cancel{ ({x}^{} - 2)}} \: \\ \\ \\ \large \longrightarrow \rm \lim \limits_{ \rm x \rightarrow2} \: \dfrac{ x + 2}{ {x}^{2} } \: \\ \\ \\ \large \longrightarrow \rm \dfrac{2 + 2}{ {2}^{2} } \\ \\ \\ \large \longrightarrow \rm \dfrac{4}{ 4} \\ \\ \\ \large \longrightarrow \rm 1$