Science:Math Exam Resources/Courses/MATH100/December 2010/Question 01 (a)/Solution 1

Directly plugging in x=1 into the limit gives 0/0. We try to factor to cancel out the terms making the fraction zero.

$\displaystyle {\begin{aligned}&\lim _{x\to 1}{\frac {x^{2}+2x-3}{x-1}}\\=&\lim _{x\to 1}{\frac {(x-1)(x+3)}{x-1}}\\=&\lim _{x\to 1}(x+3)\\=&(1)+3\\=&4\end{aligned}}$