What is the quotient when (1/x - 1) is divided by (x-1) ?
[1/x]square+1
1/x-1=(1-x)/x=-(x-1)/x
( 1/x - 1)/(x-1)
= ((1-x)/x)/(x-1)
= (1-x)/x * 1/(x-1)
= -1/x
To find the quotient when (1/x - 1) is divided by (x-1), we can use long division.
Step 1: Write the expression (1/x - 1) as a fraction over a common denominator.
(1/x - 1) = (1 - x)/x
Step 2: Divide the numerator (1 - x) by the denominator (x-1) using long division.
___________________
(x - 1) | (1 - x)
- (x - 1)
Step 3: Subtract (x - 1) from (1 - x).
___________________
(x - 1) | (1 - x)
- (x - 1)
____________
-2
The quotient is -2.