Saved Bookmarks
| 1. |
Simplify:x/x - y + y/x + y + 2xy/x2 + y2\(\frac{x}{x-y}+\frac{y}{x+y}+\frac{2xy}{x^2+y^2}\) |
|
Answer» \(\frac{x}{x-y}+\frac{y}{x+y}+\frac{2xy}{x^2+y^2}\) = \(\frac{x(x+y)+y(x-y)}{(x-y)(x+y)}+\frac{2xy}{x^2+y^2}\) = \(\frac{x^2+xy+xy-y^2}{x^2-y^2}+\frac{2xy}{x^2+y^2}\) = \(\frac{x^2+2xy-y^2+(x^2+y^2)+2xy(x^2-y^2)}{(x^2-y^2)(x^2+y^2)}\) = \(\frac{x^4+2x^3y-x^2y^2+x^2y^2+2xy^3-y^4+2x^3y+2xy^3}{x^4-y^4}\) = \(\frac{x^4+4x^3y-y^4}{x^4-y^4}\) |
|