\(1)\ \frac{b+4}{b^2-6b+9}:\frac{b^2-16}{2b-6}-\frac{2}{b-4}=\frac{2}{3-b}\)
\(1)\ \frac{b+4}{b^2-6b+9}:\frac{b^2-16}{2b-6}=\frac{b+4}{ (b-3)^2}\cdot\frac{ 2(b-3)}{ (b-4)(b+4)}=\frac{2}{ (b-3)(b-4)}\)
\(2)\ {\frac{2}{ (b-3)(b-4)}}^{\backslash1}-{\frac{2}{b-4}}^{\backslash{b\ -\ 3}}=\frac{2-(2b-6)}{ (b-3)(b-4)}=\frac{2-2b+6}{ (b-3)(b-4)}=\frac{8-2b}{ (b-3)(b-4)}=\frac{ {-}2(b-4)}{ (b-3)(b-4)}={-}\frac{2}{b-3}=\frac{2}{3-b}\)
\(2)\ \left(\frac{m-1}{m+1}-\frac{m+1}{m-1}\right):\frac{4m}{m^2-1}={-}1\)
\(1)\ {\frac{m-1}{m+1}}^{\backslash{m\ -\ 1}}-{\frac{m+1}{m-1}}^{\backslash{m\ +\ 1}}=\frac{ (m-1)^2-(m+1)^2}{ (m-1)(m+1)}=\frac{m^2-2m+1-(m^2+2m+1)}{ (m-1)(m+1)}=\frac{m^2-2m+1-m^2-2m-1}{ (m-1)(m+1)}=\frac{{-}4m}{ (m-1)(m+1)}={-}\frac{4m}{ (m-1)(m+1)}\)
\(2)\ {-}\frac{4m}{ (m-1)(m+1)}:\frac{4m}{m^2-1}={-}\frac{4m}{m^2-1}\cdot\frac{m^2-1}{4m}={-}1\)
\(3)\ \frac{2x}{x^2-y^2}:\left(\frac{1}{x^2+2xy+y^2}-\frac{1}{y^2-x^2}\right)=x+y\)
\(1)\ \frac{1}{x^2+2xy+y^2}-\frac{1}{y^2-x^2}=\frac{1}{x^2+2xy+y^2}-\frac{1}{ {-}(x^2-y^2)}={\frac{1}{ (x+y)^2}}^{\backslash{x\ -\ y}}+{\frac{1}{ (x-y)(x+y)}}^{\backslash{x\ +\ y}}=\frac{x-y+x+y}{ (x+y)^2(x-y)}=\frac{2x}{ (x+y)^2(x-y)}\)
\(2)\ \frac{2x}{x^2-y^2}:\frac{2x}{ (x+y)^2(x-y)}=\frac{2x}{ (x-y)(x+y)}\cdot\frac{ (x+y)^2(x-y)}{2x}=x+y\)
\(4)\ \left(\frac{2a-3}{a^2-4a+4}-\frac{a-1}{a^2-2a}\right):\frac{a^2-2}{a^3-4a}=\frac{a+2}{a-2}\)
\(1)\ \frac{2a-3}{a^2-4a+4}-\frac{a-1}{a^2-2a}={\frac{2a-3}{ (a-2)^2}}^{\backslash{a}}-{\frac{a-1}{ a(a-2)}}^{\backslash{a\ -\ 2}}=\frac{2a^2-3a-(a^2-2a-a+2)}{ a(a-2)^2}=\frac{2a^2-3a-a^2+2a+a-2}{ a(a-2)^2}=\frac{a^2-2}{ a(a-2)^2}\)
\(2)\ \frac{a^2-2}{ a(a-2)^2}:\frac{a^2-2}{a^3-4a}=\frac{a^2-2}{ a(a-2)^2}\cdot\frac{ a(a^2-4)}{a^2-2}=\frac{a^2-2}{ a(a-2)^2}\cdot\frac{ a(a-2)(a+2)}{a^2-2}=\frac{a+2}{a-2}\)
