dividing fractions with x

Question

(x^2 -1)/(x-1) 

 

can I divide the X^2 by the x, and the -1 by the -1 to give me  x+1, or do I need to separate it into 

 

x^2/(x-1)  and -1/(x-1)  to get 

 

-x + -1/(x-1)

Answer 1

The way to simplify this expression is to factor the numerator as a difference of squares, and then divide by the denominator:

 

x^2 - 1 = (x - 1)(x + 1)

 

Therefore,

 

(x^2 - 1) / (x - 1) = [(x - 1)(x + 1)] / (x - 1) = x + 1

Answer 2

The numerator is the difference of a perfect square binomial. In other words, the numerator can be factored into (X-1)(X+1)

 

then the X-1 is a common factor so the fraction reduces to just 

X+1 In the numera as the final answer. 

Answer 3

Reducing a fraction with common factors:

(x² - 1) / (x - 1)

(x + 1)(x - 1) / (x - 1)

x + 1

 

Doing long division:

           x  + 1

x - 1  | x²      - 1

           x² - x

                  x - 1

                  x - 1

                     0