What is the answer to (m(x+n)-n(x-m))/(m(m+n)+n(n-m))=1 ?

The answer to (m(x+n)-n(x-m))/(m(m+n)+n(n-m))=1 is x=m-n;\quad m(m+n)+n(n-m)\ne 0,m\ne n

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(m(x+n)-n(x-m))/(m(m+n)+n(n-m))=1

\frac{m ( x + n ) - n ( x - m )}{m ( m + n ) + n ( n - m )} = 1

x = m - n; m (m + n) + n (n - m) \neq = 0, m \neq = n

Solution steps

\frac{m ( x + n ) - n ( x - m )}{m ( m + n ) + n ( n - m )} = 1

Multiply both sides by

m (m + n) + n (n - m)

m x - n x + 2 mn = m^{2} + n^{2}; m (m + n) + n (n - m) \neq = 0

Move

2 mn

to the right side

m x - n x = m^{2} + n^{2} - 2 mn; m (m + n) + n (n - m) \neq = 0

Factor

m x - n x : x (m - n)

x (m - n) = m^{2} + n^{2} - 2 mn; m (m + n) + n (n - m) \neq = 0

Divide both sides by

m - n; m (m + n) + n (n - m) \neq = 0, m \neq = n

x = m - n; m (m + n) + n (n - m) \neq = 0, m \neq = n

b, \frac{a - b}{c + d} = f

- 7 x + 16 = 58

5 (p - 3) = 63

0 = - 2 x

x, 3 x + 3 y = 0

What is the answer to (m(x+n)-n(x-m))/(m(m+n)+n(n-m))=1 ?
The answer to (m(x+n)-n(x-m))/(m(m+n)+n(n-m))=1 is x=m-n;\quad m(m+n)+n(n-m)\ne 0,m\ne n