Question

Выражение (a-b+4ab/(a-b))/(a/(a+b)-2ab/(b2-a2))

Answer 1

$\frac{(a-b+ \frac{4ab}{a-b} )}{ \frac{a}{a+b} - \frac{2ab}{ b^{2} - a^{2} } } = \frac{(\frac{ (a-b)^{2} +4ab}{a-b} )}{ \frac{a}{a+b} - \frac{2ab}{ (b-a)(b+a) } } =$$\frac{(\frac{ a^{2} -2ab+ b^{2} +4ab}{a-b} )}{ \frac{a(b-a)-2ab}{ (b-a)(b+a) } } =$$=\frac{(a^{2} +2ab+ b^{2} )(b+a)}{ab- a^{2}-2ab } = \frac{ (a+b)^{2}(a+b) }{- a^{2} -ab} = -\frac{ (a+b)^{3} }{a(a+b)} =-\frac{ (a+b)^{2} }{a}$