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Lim x—> -2
sqrt(3x+10) -2/ x+2

User YBathia
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\displaystyle\lim_(x\to-2)(√(3x+10)-2)/(x+2)

Rationalize the numerator:


(√(3x+10)-2)/(x+2)\cdot(√(3x+10)+2)/(√(3x+10)+2)=((3x+10)-4)/((x+2)(√(3x+10)+2))=\frac3{√(3x+10)+2}

where the
x+2 factors in the numerator and denominator cancel. Then the limit is


\displaystyle\lim_(x\to-2)(√(3x+10)-2)/(x+2)=\lim_(x\to-2)\frac3{√(3x+10)+2}=\frac3{\sqrt4+2}=\boxed{\frac34}

User StackoverBlows
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