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Evaluate: ("lim")(xveca)(sqrt(a+2x)-sqrt...

Evaluate: `("lim")_(xveca)(sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x)),(a!=0)dot`

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`lim_(xtoa)((sqrt(a+2x)-sqrt(3x)))/((sqrt(3a+x)-2sqrtx))`
`=lim_(xtoa)((sqrt(a+2x)-sqrt(3x)))/((sqrt(3a+x)-2sqrtx))xx((sqrt(3a+x)+2sqrtx))/((sqrt(3a+x)+2sqrtx))xx((sqrt(a+2x)+sqrt(3x)))/((sqrt(a+2x)+sqrt(3x)))`
`lim_(xtoa)([(a+2x)-3x]xx(sqrt(3a+x)+2sqrtx))/([(3a+x)-4x]xx(sqrt(a+2x)+sqrt(3x)))`
`=lim_(xtoa)((a-x)xx(sqrt(3a+x)+2sqrtx))/(3(a-x)xx(sqrt(a+2x)+sqrt(3x)))=lim_(xtoa)((sqrt(3a+x)+sqrt(3x)))/((sqrt(a+2x)+sqrt(3x)))`
`=((sqrt(4a)+2sqrta))/(3(sqrt(3a)+sqrt(3a)))=(4sqrta)/(6sqrt3sqrta)=(1)/(3sqrt3).`
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