Question

giới hạn \(\lim\limits_{x\rightarrow3}\dfrac{x+1-\sqrt{5x+1}}{x-\sqrt{4x-3}}=\dfrac{a}{b}\). tìm a,b biết a/b tối giản

Answer 1

\(\lim\limits_{x\rightarrow3}\dfrac{\left(x^2+2x+1-5x-1\right)\left(x+\sqrt{4x-3}\right)}{\left(x^2-4x+3\right)\left(x+1+\sqrt{5x+1}\right)}\)

\(=\lim\limits_{x\rightarrow3}\dfrac{x\left(x-3\right)\left(x+\sqrt{4x-3}\right)}{\left(x-1\right)\left(x-3\right)\left(x+1+\sqrt{5x+1}\right)}\)

\(=\lim\limits_{x\rightarrow3}\dfrac{x\left(x+\sqrt{4x-3}\right)}{\left(x-1\right)\left(x+1+\sqrt{5x+1}\right)}=\dfrac{9}{8}\)