What is the limit as x approaches 2 of ((x-2))/((sqrt(x-1)-\sqrt{3-x))} ?

The limit as x approaches 2 of ((x-2))/((sqrt(x-1)-\sqrt{3-x))} is 1

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limit as x approaches 2 of ((x-2))/((sqrt(x-1)-\sqrt{3-x))}

x \to 2 lim (\frac{( x - 2 )}{( x - 1 - 3 - x )})

1

Solution steps

x \to 2 lim (\frac{x - 2}{x - 1 - 3 - x})

Rationalize denominator

\frac{x - 2}{x - 1 - 3 - x} : \frac{x - 1 + - x + 3}{2}

= x \to 2 lim (\frac{x - 1 + - x + 3}{2})

Plug in the value

x = 2

= \frac{2 - 1 + - 2 + 3}{2}

Simplify

\frac{2 - 1 + - 2 + 3}{2} : 1

= 1

What is the limit as x approaches 2 of ((x-2))/((sqrt(x-1)-\sqrt{3-x))} ?
The limit as x approaches 2 of ((x-2))/((sqrt(x-1)-\sqrt{3-x))} is 1