EXPLANATION.\sf \implies \lim_{x \to - 6 } \dfrac{\SQRT{(10 - x} - 4}{x + 6}.⟹lim x→−6 x+6(10−x −4 .As we know that,Put the values of x = -6 in equation, we get.\sf \implies \lim_{x \to - 6} \dfrac{\sqrt{10 - (-6)} - 4}{(- 6 + 6)}.⟹lim x→−6 (−6+6)10−(−6) −4 .\sf \implies \lim_{x \to - 6} \dfrac{4 - 4}{- 6 + 6}.⟹lim x→−6 −6+64−4 .\sf \implies \lim_{x \to - 6} \dfrac{0}{0}.⟹lim x→−6 00 .As we can see that it is in the form of 0/0.We can simply factorizes the equation.But if root is in 0/0 form we can simply rationalizes the equation, we get.Rationalizes the equation, we get.\sf \implies \lim_{x \to - 6} \dfrac{\sqrt{10 - x} - 4}{x + 6} \ X \ \dfrac{\sqrt{10 - x} + 4}{\sqrt{10 - x} + 4}.⟹lim x→−6 x+610−x −4 X 10−x +410−x +4 .\sf \implies \lim_{x \to - 6} \dfrac{(\sqrt{10 - x})^{2} - (4)^{2} }{(x + 6) (\sqrt{10 - x} + 4)} .⟹lim x→−6 (x+6)( 10−x +4)( 10−x ) 2 −(4) 2 .\sf \implies \lim_{x \to - 6} \dfrac{(10 - x) - 16}{(x + 6) (\sqrt{10 - x } + 4)}.⟹lim x→−6 (x+6)( 10−x +4)(10−x)−16 .\sf \implies \lim_{x \to - 6} \dfrac{- x - 6}{(x + 6)(\sqrt{10 - x} + 4)}.⟹lim x→−6 (x+6)( 10−x +4)−x−6 .\sf \implies \lim_{x \to - 6} \dfrac{-(x + 6)}{(x + 6)(\sqrt{10 - x} + 4)}.⟹lim x→−6 (x+6)( 10−x +4)−(x+6) .\sf \implies \lim_{x \to - 6} \dfrac{- 1}{(\sqrt{10 - x } + 4)}.⟹lim x→−6 ( 10−x +4)−1 .Put the VALUE of x = -6 in equation, we get.\sf \implies \lim_{x \to - 6} \dfrac{- 1}{(\sqrt{10 - (- 6)} +4) }.⟹lim x→−6 ( 10−(−6) +4)−1 .\sf \implies \lim_{x \to - 6} \dfrac{- 1}{(\sqrt{16} + 4)}.⟹lim x→−6 ( 16 +4)−1 .\sf \implies \lim_{x \to - 6} \dfrac{- 1}{8}.⟹lim x→−6 8−1 .\sf \implies values \ of \ equation \lim_{x \to - 6} \dfrac{\sqrt{10 - x} - 4}{x + 6} = \dfrac{- 1}{8}.⟹values of equationlim x→−6 x+610−x −4 = 8−1 .