Question

adição algebrica--- $1+ \frac{x²-y²}{y²}$

Answer 1

$1+\dfrac{x^{2}-y^{2}}{y^{2}}=\dfrac{1}{1}+\dfrac{x^{2}-y^{2}}{y^{2}}$

O mmc entre 1 e y² é y². Portanto:

$1+\dfrac{x^{2}-y^{2}}{y^{2}}=\dfrac{y^{2}}{y^{2}}+\dfrac{x^{2}-y^{2}}{y^{2}}\\\\\\1+\dfrac{x^{2}-y^{2}}{y^{2}}=\dfrac{y^{2}+x^{2}-y^{2}}{y^{2}}\\\\\\1+\dfrac{x^{2}-y^{2}}{y^{2}}=\dfrac{x^{2}}{y^{2}}\\\\\\\boxed{\boxed{1+\dfrac{x^{2}-y^{2}}{y^{2}}=\left(\dfrac{x}{y}\right)^{2}}}$