Question

Sabendo que x-y= 10, qual é o valor numérico da expressão x²y3/y2+xy ×(1/x² - 1/y²)
com calculooo plsss
urgenteeee​

Answer 1

Resposta: - 10.

         $\dfrac{x^2y^3}{y^2+xy}\cdot\bigg(\dfrac{1}{x^2}-\dfrac{1}{y^2}\bigg)~~\Longleftrightarrow$

$\Longleftrightarrow~~\dfrac{x^2y^2}{y+x}\cdot\bigg(\dfrac{y^2}{x^2y^2}-\dfrac{x^2}{x^2y^2}\bigg)~~\Longleftrightarrow$

$\Longleftrightarrow~~\dfrac{x^2y^2}{y+x}\cdot\dfrac{y^2-x^2}{x^2y^2}~~\Longleftrightarrow$

$\Longleftrightarrow~~\dfrac{\cancel{x^2y^2}(y^2-x^2)}{(y+x)\cancel{x^2y^2}},~~x^2y^2\neq0~~\Longleftrightarrow$

$\Longleftrightarrow~~\dfrac{y^2-x^2}{y+x}~~\Longleftrightarrow$

$\Longleftrightarrow~~\dfrac{\cancel{(y+x)}(y-x)}{\cancel{y+x}},~~y+x\neq0~~\Longleftrightarrow$

$\Longleftrightarrow~~y-x$

Se x - y = 10, então y - x = - 10.

$\therefore~\dfrac{x^2y^3}{y^2+xy}\cdot\bigg(\dfrac{1}{x^2}-\dfrac{1}{y^2}\bigg)=y-x=-\,10.$