Bruch kürzen: (x - y·x^{1/2}) / (y - x^{1/2})

Question

(x - y·x^{1/2}) / (y - x^{1/2}) verwirrt mich.

laut Wolfram-Alpha kommt -wurzel x raus. Wenn man dies kürzt.

$$\frac { x-y\sqrt { x }  }{ y-\sqrt { x }  } $$

Answer 1

(x - y·x^{1/2}) / (y - x^{1/2})

= -(y·x^{1/2} - x) / (y - x^{1/2})

= -x^{1/2}·(y - x^{1/2}) / (y - x^{1/2})

= -x^{1/2}