Given:

▪
$\bold{(2x-5)/(x^(2) -2)}$

▪
$\bold{(dy)/(dx)}$

$\huge\mathbb{ \underline{SOLUTION :}}$

»
$\tt{For \: \: y,}$

$\longrightarrow\sf{y=v \frac{2x - 5}{ {x}^(2) - 2} }$

$\longrightarrow\sf{(dy)/(dx) = \cfrac{ ( {x}^(2) - 2)(2) - (2x - 5)(2x)}{( {x}^(2) - {2}^(2) )}}$

$\longrightarrow\sf{\cfrac{2 {x}^(2) - 4 - {4x}^(2) + 10x}{ ({x}^(2) - {2}^(2) )}}$

$\longrightarrow{={ \boxed{\sf \cfrac{ - 2 {x}^(2) - 4 + 10x}{ ({x}^(2) - {2}^(2) )}}}}$

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$\tt{At \: \: x = 2,}$

$\longrightarrow\sf{ \frac{ - 2(2) {}^(2) + 10(2) - 4 }{( {2}^(2) - 2 {)}^(2) } }$

$\longrightarrow\sf{( - 8 + 20 - 4)/(4) }$

$\longrightarrow\sf{ (8)/(4) }$

$\longrightarrow{\sf = \boxed{\sf {2}}}$ ✓

$\huge \mathbb{ \underline{ANSWER:}}$

◆ The value of the given differential function at
$\sf{x=2}$ is
$\sf{2.}$

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