What is the simplified form of x over x^2- y^2 + y over x^2- y^2?
Since you already have a common denominator, you can add the fractions directly:
[x / (x^2 - y^2)] + [y / (x^2 - y^2)] = (x + y) / (x^2 - y^2)
Factor the denominator using the difference-of-squares formula a^2 - b^2 = (a + b)(a - b):
x^2 - y^2 = (x + y)(x - y)
That makes the fraction:
(x + y) / [(x + y)(x - y)]
Factor out (cancel) the common (x + y) term to get:
1 / (x - y)
Comments
Since you already have a common denominator, you can add the fractions directly:
[x / (x^2 - y^2)] + [y / (x^2 - y^2)] = (x + y) / (x^2 - y^2)
Factor the denominator using the difference-of-squares formula a^2 - b^2 = (a + b)(a - b):
x^2 - y^2 = (x + y)(x - y)
That makes the fraction:
(x + y) / [(x + y)(x - y)]
Factor out (cancel) the common (x + y) term to get:
1 / (x - y)