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.