Solución problema 4.

Enunciado problema 4

Como

$$\frac{x^2}{y^2}-\frac{y^2}{x^2}=\frac{x^4-y^4}{{\left(xy\right)}^2}=\frac{\left(x^2+y^2\right)\left(x^2-y^2\right)}{{\left(xy\right)}^2}=$$

$$=\frac{\left[{\left(x+y\right)}^2-2xy\right]\left(x+y\right)\left(x-y\right)}{{\left(xy\right)}^2}=\frac{\left(a-\frac{a-b}{2}\right)\sqrt{ab}}{{\left(\frac{a-b}{4}\right)}^2}$$