Question

$\underset{x\to 1}{lim}\left(\frac{3-5\frac{1}{1-x}}{3+5\frac{1}{1-x}}\right)$ is equal to

• A. $2$
• B. $0$
• C. $1$
• D. $-1$

Answer 1

The correct option is D $-1$

$\underset{x\to 1}{lim}\left(\frac{3-5\frac{1}{1-x}}{3+5\frac{1}{1-x}}\right)$

$=\underset{x\to 1}{lim}\left(\frac{3(1-x)-5}{3(1-x)+5}\right)$

$=\underset{x\to 1}{lim}\left(\frac{3-3x-5}{3-3x+5}\right)$

$=\underset{x\to 1}{lim}\left(\frac{-2-3x}{8-3x}\right)$

$⟹\frac{-2-3}{8-3}$

$⟹-1$