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]
