Question

if x^(-1) - 1 is divided by x - 1 then the quotient is?​

Answer 1

Answer:

$- {x}^{ - 1}$

Step-by-step explanation:

$( {x}^{ - 1} - 1) = (1 \div x - 1) \\ = (1 - x) \div x = - (x - 1) \div x$

Now,

$( {x}^{ - 1} - 1) \div (x - 1) \\ = - ((x - 1) \div x) \div ( x - 1) \\ = - 1 \div x = - {x }^{ - 1}$