# How do you find the limit of #((root3 x) -1)/((sqrt x) -1)# as x approaches 1?

Rationalize and reduce.

and

So,

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To find the limit of ((√3x) - 1)/((√x) - 1) as x approaches 1, we can use algebraic manipulation. By multiplying the numerator and denominator by the conjugate of (√x) - 1, we can simplify the expression. After simplification, we can substitute x = 1 into the expression to find the limit. The limit of ((√3x) - 1)/((√x) - 1) as x approaches 1 is 2√3.

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