Question

упростите выражение 7. Упростите выражение:

ba
bba

ab
b
bab
a














)(
,
0a
,
0b
,

Answer 1

Ответ:

$(\frac{a}{\sqrt{ab} -b} - \frac{\sqrt{b} }{\sqrt{b} -\sqrt{a} } )*\frac{(\sqrt{a} -\sqrt{b})b }{a+b} = \frac{a*(\sqrt{b}-\sqrt{a})-(\sqrt{ab}-b)\sqrt{b} }{(\sqrt{ab}-b )*(\sqrt{b}-\sqrt{a} )} * \frac{(\sqrt{a} -\sqrt{b})b}{a+b} =\frac{a\sqrt{b}-a\sqrt{a} -(\sqrt{ab^2} -b\sqrt{b})}{(\sqrt{ab}-b)*(\sqrt{b}-\sqrt{a} ) } * \frac{(\sqrt{a}-\sqrt{b} )b }{a+b} =\frac{a\sqrt{b}-a\sqrt{a}-(b\sqrt{a} -b\sqrt{b}) }{(\sqrt{ab} -b)*(\sqrt{b}-\sqrt{a}) } * \frac{(\sqrt{a}-\sqrt{b})b }{a+b} =$$= \frac{a\sqrt{b}-a\sqrt{a} -b\sqrt{a}+b\sqrt{b} }{(\sqrt{ab} -b)*(\sqrt{b}-\sqrt{a}) } * \frac{(\sqrt{a} -\sqrt{b})b}{a+b} =\frac{a*(\sqrt{b}-\sqrt{a})+b*(-\sqrt{a} +\sqrt{b}) }{(\sqrt{ab} -b)*(\sqrt{b}-\sqrt{a} )} * \frac{(\sqrt{a}-\sqrt{b})b }{a+b} =\frac{(\sqrt{b}-\sqrt{a} )*(a+b)}{(\sqrt{ab}-b)*(\sqrt{b}-\sqrt{a} ) } * \frac{(\sqrt{a}-\sqrt{b})b }{a+b} =$$= \frac{a+b}{\sqrt{ab} -b} *\frac{(\sqrt{a}-\sqrt{b})b }{a+b} =\frac{1}{\sqrt{b}*(\sqrt{a}-\sqrt{b}) } *(\sqrt{a} -\sqrt{b})b=\frac{1}{\sqrt{b}} *b=\frac{b}{\sqrt{b}} =\sqrt{b}$