Answer
$5$
Work Step by Step
$\lim _{x\rightarrow 1}\dfrac {\sqrt {10x-9}-1}{x-1}=\lim _{x\rightarrow 1}\dfrac {\sqrt {10x-9}-1}{\left( x-1\right) }\times \dfrac {\sqrt {10x-9}+1}{\sqrt {10x-9}+1}=\dfrac {\left( \sqrt {10x-9}\right) ^{2}-1^{2}}{\left( x-1\right) \sqrt {10x-9}+1}=\dfrac {10\left( x-1\right) }{\left( x-1\right) \left( \sqrt {10x-9}+1\right) }=\dfrac {10}{\sqrt {10-9}+1}=\dfrac {10}{2}=5 $
