Find the limit by rewriting the fraction first.

ModifyingBelow lim With Start $2$ By $1$ Matrix $1$st Row $1$st Column left parenthesis x comma y right parenthesis right arrow left parenthesis $0$ comma $0$ right parenthesis $2$nd Row $1$st Column x not equals y EndMatrixlim

$($x$,$y$)(0,0)$x$$y

StartFraction x minus y plus $2$ StartRoot x EndRoot minus $2$ StartRoot y EndRoot Over StartRoot x EndRoot minus StartRoot y EndRoot EndFractionx$$y$+2$x$2$yx$$y

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Part $1$

ModifyingBelow lim With Start $2$ By $1$ Matrix $1$st Row $1$st Column left parenthesis x comma y right parenthesis right arrow left parenthesis $0$ comma $0$ right parenthesis $2$nd Row $1$st Column x not equals y EndMatrixlim

$($x$,$y$)(0,0)$x$$y

StartFraction x minus y plus $2$ StartRoot x EndRoot minus $2$ StartRoot y EndRoot Over StartRoot x EndRoot minus StartRoot y EndRoot EndFractionx$$y$+2$x$2$yx$$yequals$=$enter your response here

$($Simplify your answer. Type an exact$$ answer, using radicals as$$ needed.$)$