Answer:[tex]m=-\frac{3}{2}[/tex]Step-by-step explanation:The given equation is [tex]\frac{m}{m+1}+\frac{5}{m-1}=1[/tex]The Least Common Denominator is [tex](m-1)(m+1)[/tex].We multiply through by the LCD to get;[tex](m-1)(m+1)\times \frac{m}{m+1}+(m-1)(m+1)\times\frac{5}{m-1}=(m-1)(m+1)\times1[/tex]Simplify[tex](m-1)\times \frac{m}{1}+(1)(m+1)\times\frac{5}{1}=(m-1)(m+1)\times1[/tex][tex]m(m-1)+5(m+1)=(m-1)(m+1)[/tex]Expand;(Use difference of two squares on the right hand side)[tex]m^2-m+5m+5=m^2-1[/tex]Group similar terms;[tex]m^2-m^2-m+5m=-1-5[/tex]Simplify;[tex]4m=-6[/tex]Divide through by 4.[tex]m=\frac{-6}{4}[/tex][tex]m=-\frac{3}{2}[/tex]