Simplify \(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x - y}\)
A
\(\frac{x^2 + y^2} {(x - y)^2}\)
B
\(\frac{2y^3} {y^2 - x^2}\)
C
\(\frac{3x^2 + y^2} {(2x - y)^2}\)
D
\(\frac{x^2 + y^2} {(x^2 - y)}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{x^2 + y^2 + xy}{x + y}\) - \(\frac{x^2 + y^2}{x -y}\)
= \(\frac{-y^3 - y^3}{x^2 - y^2}\)
= \(\frac{2y^3}{x^2 - y^2}\)
= \(\frac{2y^3}{y^2 - x^2}\)
Source: Myschool Past Questions Archive (Record #32660)