# How do you find the limit of #(sqrt(x+8)-3)/(x-1)# as #x->1#?

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To find the limit of (sqrt(x+8)-3)/(x-1) as x approaches 1, we can use algebraic manipulation and the concept of limits. By factoring the numerator as (sqrt(x+8)-3) = (sqrt(x+8)-3)(sqrt(x+8)+3), we can simplify the expression to (x+8-9)/(x-1)(sqrt(x+8)+3). Canceling out the (x-1) terms, we are left with (1)/(sqrt(x+8)+3). Substituting x=1 into this expression, we get 1/(sqrt(1+8)+3) = 1/(sqrt(9)+3) = 1/(3+3) = 1/6. Therefore, the limit of (sqrt(x+8)-3)/(x-1) as x approaches 1 is 1/6.

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