Question

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

• A. 1
• B. -1
• C. 0
• D. does not exist

Answer 1

Answer: (B)

-1

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

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

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

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

$⟹\frac{-2-3}{8-3}$

$⟹-1$