What is the answer to ((x-1))/((2n+1))+((2n+1))/((n-1))=2 ?

The answer to ((x-1))/((2n+1))+((2n+1))/((n-1))=2 is x=4n+3-((2n+1)^2)/(n-1);\quad n\ne-1/2

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((x-1))/((2n+1))+((2n+1))/((n-1))=2

\frac{( x - 1 )}{( 2 n + 1 )} + \frac{( 2 n + 1 )}{( n - 1 )} = 2

x = 4 n + 3 - \frac{( 2 n + 1 ) ^{2}}{n - 1}; n \neq = - \frac{1}{2}

Solution steps

\frac{( x - 1 )}{( 2 n + 1 )} + \frac{( 2 n + 1 )}{( n - 1 )} = 2

\frac{x - 1}{2 n + 1} + \frac{2 n + 1}{n - 1} = 2

Move

\frac{2 n + 1}{n - 1}

to the right side

\frac{x - 1}{2 n + 1} = 2 - \frac{2 n + 1}{n - 1}

Multiply both sides by

2 n + 1

x - 1 = 2 (2 n + 1) - \frac{( 2 n + 1 ) ^{2}}{n - 1}; n \neq = - \frac{1}{2}

Move

1

to the right side

x = 4 n + 3 - \frac{( 2 n + 1 ) ^{2}}{n - 1}; n \neq = - \frac{1}{2}

\frac{x + 7}{3} = \frac{1 + 3 x - 2}{5}

2 x + 12 + 5 x - (- 2) = x

z = (3 - 4 i) (12 + 5 i)

\frac{4}{5} = 100 - \frac{x}{100} + 5 \frac{x}{3}

z + 3 = \frac{2 ( 1 - 3 z )}{3}

What is the answer to ((x-1))/((2n+1))+((2n+1))/((n-1))=2 ?
The answer to ((x-1))/((2n+1))+((2n+1))/((n-1))=2 is x=4n+3-((2n+1)^2)/(n-1);\quad n\ne-1/2