Question

. Determine 〖 lim 〗┬(x→1) (1/(x-1)+(x-5)/(x^2+2x-3))

Answer 1

$lim_{x \: \to \: 1} (\frac{1}{ x - 1 } + \frac{x - 5}{ {x}^{2} + 2x - 3} ) = \\ lim_{x \: \to \: 1} (\frac{1}{ x - 1 } + \frac{x -5}{ (x - 1)(x + 3)} ) = \\lim_{x \: \to \: 1} (\frac{x + 3 + x - 5}{ (x - 1)(x + 3) }) = \\lim_{x \: \to \: 1} (\frac{2(x - 1)}{ (x - 1)(x + 3)} ) = \\lim_{x \: \to \: 1} (\frac{2}{ x + 3 } ) = \frac{1}{2}$