Question

Розв'яжіть будьласка☺даю29 балів

Answer 1

$1)\frac{a}{ab-b^{2}}-\frac{b}{a^{2}-ab}=\frac{a}{b(a-b)}-\frac{b}{a(a-b)}=\frac{a^{2}-b^{2} }{ab(a-b)}=\frac{(a-b)(a+b)}{ab(a-b)}=\frac{a+b}{ab}\\\\\frac{a+b}{ab}:\frac{1}{ab}=\frac{a+b}{ab}*ab=a+b\\\\a+b=-3\frac{5}{7}+3\frac{5}{7}=0\\\\Otvet:\boxed{0}$

$2)\frac{15y-1}{2y+1}+\frac{15y-4}{2y-1}-\frac{3}{1-4y^{2}}=0\\\\\frac{15y-1}{2y+1}+\frac{15y-4}{2y-1}+\frac{3}{(2y+1)(2y-1)}=0\\\\\frac{30y^{2}-15y-2y+1+30y^{2}+15y-8y-4+3}{(2y+1)(2y-1)}=0\\\\\frac{60y^{2}-10y }{(2y+1)(2y-1)}=0$

$\left \{ {{60y^{2}-10y=0} \atop {2y+1\neq0;2y-1\neq0}} \right.\\\\\left \{ {{6y^{2}-y=0 } \atop {y\neq-0,5,y\neq0,5}} \right.\\\\6y^{2}-y=0\\\\y(6y-1)=0\\\\y_{1}=0\\\\6y-1=0\\\\y_{2}=\frac{1}{6}\\\\Otvet:\boxed{0;\frac{1}{6}}$

$3)\frac{1}{m-n}*(\frac{m^{2}}{n}-\frac{n^{2}}{m})= \frac{1}{m-n}*\frac{m^{3}-n^{3}}{mn}=\frac{(m-n)(m^{2}+mn+n^{2})}{(m-n)*mn}=\frac{m^{2}+mn+n^{2}}{mn}\\\\\frac{m^{2}-n^{2}}{mn}-\frac{m^{2}+mn+n^{2}}{mn}=\frac{m^{2}-n^{2}-m^{2}-mn-n^{2} }{mn}=\frac{-2n^{2}-mn }{mn}=-\frac{n(2n+m)}{mn}\\\\-\frac{n(2n+m)}{mn}*\frac{1}{m+2n}=-\frac{1}{m}$