Question

Find the missing term.

Answer 1

Equations are used to relate equal expressions.

The missing term is: $\mathbf{ m -1}$

The equation is given as:

$\mathbf{\frac{m - n}{m^2 - n^2} + \frac{?}{(m -1)(m -n)} = \frac{2m}{m^2 - n^2}}$

Express $\mathbf{m^2 - n^2\ as\ (m - n)(m + n)}$

So, we have:

$\mathbf{\frac{m - n}{(m - n)(m + n)} + \frac{?}{(m -1)(m -n)} = \frac{2m}{(m - n)(m + n)}}$

Multiply through by $\mathbf{m - n}$

$\mathbf{\frac{m - n}{m + n} + \frac{?}{m -1} = \frac{2m}{m + n}}$

Collect like terms

$\mathbf{ \frac{?}{m -1} = \frac{2m}{m + n} - \frac{m - n}{m + n}}$

Take LCM

$\mathbf{ \frac{?}{m -1} = \frac{2m - m + n}{m + n} }$

$\mathbf{ \frac{?}{m -1} = \frac{m + n}{m + n} }$

Divide $\mathbf{ \frac{m + n}{m + n} }$

$\mathbf{ \frac{?}{m -1} = 1}$

Cross multiply

$\mathbf{ ? =(m -1)\times 1}$

$\mathbf{ ? =m -1}$

Hence, the missing term is: $\mathbf{ m -1}$

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brainly.com/question/15668451