Simplify by writing each fraction in lowest terms:
X^2-y^2/(x-y)^2
My work: X^2-y^2/(x-y)^2
=X^2-y^2/(x-y)(x-y)
=X^2-y^2/x^2-2x2y-y^2
I don't know what to do next.
I will assume you meant:
(x^2-y^2)/(x-y)^2 , those brackets are important
= (x+y)(x-y)/(x-y)^2
= (x+y)/(x-y) , x≠y
(x^2-y^2)/(x-y)^2 = (x+y)(x-y)/(x-y)(x-y)= (x+y)/(x-y).
Recall: a^2-b^2 = (a+b)(a-b).
To simplify the fraction X^2 - y^2 / (x - y)^2, you need to factor the numerator and denominator and cancel out any common factors.
First, factor the numerator by applying the difference of squares formula:
X^2 - y^2 = (X - y)(X + y)
Next, factor the denominator:
(x - y)^2 = (x - y)(x - y)
Now, rewrite the initial expression with the factored numerator and denominator:
(X - y)(X + y) / (x - y)(x - y)
At this point, we can see that (x - y) appears in both the numerator and denominator. Therefore, we can cancel out this common factor:
(X + y) / (x - y)
This is the simplified form of the fraction.