a(squared)/(a-b)+ b(squared)/(b-a)

That equals (a^2 - b^2)/(a-b) = a + b, if simplification is what you are after.

can you please show me how you get this that's what the book says but that is not what i get...sorry for the trouble.. i want to understand it too not just have an answer

i get the a^2-b^2 / a-b... how does that turn into (a+b)

a^2 - b^2 = (a-b)(a+b)

The a-b in the denominator cancels out the one in the numerator

To simplify the expression a²/(a - b) + b²/(b - a), we can start by factoring out a negative sign from the denominator of the second fraction:

a²/(a - b) - b²/(a - b)

Next, notice that the two fractions now have a common denominator of (a - b), so we can combine them into a single fraction:

(a² - b²)/(a - b)

Now, we can use the difference of squares formula to factor the numerator as (a + b)(a - b):

((a + b)(a - b))/(a - b)

The (a - b) terms in the numerator and denominator cancel out, leaving us with:

a + b

Therefore, the simplified form of the expression is a + b.