Question

E =\frac{y-x}{y^{3} -x^{2}y} -\frac{x}{y^2-x^2}-\frac{1}{x+y}[/tex]
.
a. Simplifique a express˜ao E, e escreva a mesma como uma ´unica fração.

Answer 1

$\frac{y-x}{y^{3} -x^{2}y} -\frac{x}{y^2-x^2}-\frac{1}{x+y}\\\\\\\frac{y-x}{y(y^2-x^{2})} -\frac{x}{y^2-x^2}-\frac{1}{x+y}\\\\\\\frac{y-x}{y(x+y)(-x+y)} -\frac{x}{(x+y)(x-y)}-\frac{1}{x+y}~~\rightarrow~MMC=y(x+y)(-x+y)\\\\\\\frac{1~.~(y-x)~-~y~.~x~-~y(-x+y)~.~1}{y(x+y)(-x+y)}\\\\\\\frac{y-x~-~xy~-~(-xy+y^2)}{y(x+y)(-x+y)}\\\\\\\frac{y-x-xy+xy-y^2}{y(x+y)(-x+y)}\\\\\\\frac{-y^2-x+y}{y(x+y)(-x+y)}\\\\\\\boxed{-\frac{y^2+x-y}{y^{3} -x^{2}y}}$