Ответ:

Объяснение:

1) [tex]\frac{5}{a-b}[/tex] ·[tex]\frac{a}{a}[/tex] = [tex]\frac{5*a}{a(a-b)}[/tex]= [tex]\frac{5a}{a^{2}-ab }[/tex]

2) [tex]\frac{4}{m+n}[/tex] * [tex]\frac{m+n}{m+n}[/tex] = [tex]\frac{4*(m+n)}{(m+n)(m+n)}[/tex] = [tex]\frac{4m+4n}{(m+n)^{2} }[/tex] = [tex]\frac{4m+4n}{m^{2} +2mn+n^{2} }[/tex]

3) [tex]\frac{4}{k-1}[/tex] * [tex]\frac{k^{2} +k+1}{k^{2}+k+1 }[/tex] = [tex]\frac{4*(k^{2}+k+1) }{(k-1)(k^{2}+k+1) }[/tex] =[tex]\frac{4k^{2} +4k+4}{k^{3}-1 }[/tex]

[tex]\displaystyle\bf\\1)\\\\\frac{5}{a-b} =\frac{5\cdot a}{(a-b)\cdot a} =\frac{5a}{a^{2} -ab} \\\\\\2)\\\\\frac{4}{m+n} =\frac{4\cdot(m+n)}{(m+n)\cxdot(m+n)}=\frac{4m+4n}{m^{2} +2mn+n^{2} } \\\\\\3)\\\\\frac{4}{k-1} =\frac{4\cdot(k^{2} +k+1)}{(k-1)\cdot(k^{2}+k+1) } =\frac{4k^{2} +4k+4}{k^{3}-1 }[/tex]