How do you subtract or add algebraic fractions that have no numbers?

Question

The equation that is giving me trouble is 

 

x+y - x^2+y^2

            x-y

 

The instructions simply say: Perform the additions and subtractions indicated.

Answer 1

Hi Renee,

 

Just as with the addition of any number and a fraction you must get a common denominator and then add

 

so  if we had the following

 

4 + 1/3   We would get a common denominator of 3

 

and we would have

 

12/3 + 1/3  = 13/3

 

In this example the common denominator is (x-y)

 

so the expression becomes

 

(x+y)(x-y)/(x-y)  - (x² + y²)/(x-y)

 

this becomes

 

(x² - y²)/(x-y) - (x² + y²)/(x-y)

 

combine the numerators

 

-2y²/(x-y)

 

Hope this helps