Question

7.- Si se simplifica la expresión algebraica se obtiene :

a) 0 b) -1 c)4 d)1 e)-4

Answer 1

$E=\left(\dfrac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\left(\dfrac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2\\\\\\E=\left(\dfrac{\sqrt{a}^3+\sqrt{b}^3}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\left(\dfrac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2\\ \\\textit{Divisi\'on notable: }\dfrac{x^3+y^3}{x+y}=x^2-xy+y^2$

$E=\left[\left(\sqrt{a}^2-\sqrt{ab}+\sqrt{a}^2\right)-\sqrt{ab}\right]\left(\dfrac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2\\ \\\\E=\left(\sqrt{a}^2-2\sqrt{ab}+\sqrt{b}^2\right)\left(\dfrac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2\\ \\\\E=\left(\sqrt{a}-\sqrt{b}\right)^2\left(\dfrac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2\\ \\\\\textit{Ley de exponentes y diferencia de cuadrados: }x^2y^2=(xy)^2\\x^2-y^2=(x-y)(x+y)\\\\\boxed{E=1}$