Question

$\frac{\sqrt a + \sqrt b}{\sqrt{a} - \sqrt{b} } - \frac{2\sqrt{a^5b^5} }{a^3b^2 - a^2b^3}$

Answer 1

Ответ:

$\frac{a+b}{a-b}$

Объяснение:

$\frac{\sqrt{a}+\sqrt{b}  }{\sqrt{a}-\sqrt{b}  } -\frac{2\sqrt{a^{5}b^{5}  }}{a^{3}b^{2} -a^{2}  b^{3}  }\\\\\\\ \frac{\sqrt{a}+\sqrt{b}  }{\sqrt{a}-\sqrt{b}  } -\frac{2a^{2}b^{2}  \sqrt{ab} }{a^{2} b^{2}*(a-b) }\\\\ \frac{\sqrt{a}+\sqrt{b}  }{\sqrt{a}-\sqrt{b}  } - \frac{2\sqrt{ab} }{a-b} \\\\ \frac{\sqrt{a}+\sqrt{b}  }{\sqrt{a}-\sqrt{b}  } - \frac{2\sqrt{ab} } {(\sqrt{a}-\sqrt{b}  )*(\sqrt{a}+\sqrt{b})}\\\\\frac{(\sqrt{a}+\sqrt{b})^{2}-2\sqrt{ab}  }{(\sqrt{a}-\sqrt{b}  )*(\sqrt{a}+\sqrt{b})}$

$\frac{a+2\sqrt{ab}+b-2\sqrt{ab}  }{a-b}$

$\frac{a+b}{a-b}$