Equations are used to relate equal expressions.
The missing term is: [tex]\mathbf{ m -1}[/tex]
The equation is given as:
[tex]\mathbf{\frac{m - n}{m^2 - n^2} + \frac{?}{(m -1)(m -n)} = \frac{2m}{m^2 - n^2}}[/tex]
Express [tex]\mathbf{m^2 - n^2\ as\ (m - n)(m + n)}[/tex]
So, we have:
[tex]\mathbf{\frac{m - n}{(m - n)(m + n)} + \frac{?}{(m -1)(m -n)} = \frac{2m}{(m - n)(m + n)}}[/tex]
Multiply through by [tex]\mathbf{m - n}[/tex]
[tex]\mathbf{\frac{m - n}{m + n} + \frac{?}{m -1} = \frac{2m}{m + n}}[/tex]
Collect like terms
[tex]\mathbf{ \frac{?}{m -1} = \frac{2m}{m + n} - \frac{m - n}{m + n}}[/tex]
Take LCM
[tex]\mathbf{ \frac{?}{m -1} = \frac{2m - m + n}{m + n} }[/tex]
[tex]\mathbf{ \frac{?}{m -1} = \frac{m + n}{m + n} }[/tex]
Divide [tex]\mathbf{ \frac{m + n}{m + n} }[/tex]
[tex]\mathbf{ \frac{?}{m -1} = 1}[/tex]
Cross multiply
[tex]\mathbf{ ? =(m -1)\times 1}[/tex]
[tex]\mathbf{ ? =m -1}[/tex]
Hence, the missing term is: [tex]\mathbf{ m -1}[/tex]
Read more about equations at:
https://brainly.com/question/15668451
