What is the answer to ((2x))/((x-1))=e^2 ?

The answer to ((2x))/((x-1))=e^2 is x=(e^2)/(e^2-2)

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((2x))/((x-1))=e^2

\frac{( 2 x )}{( x - 1 )} = e^{2}

x = \frac{e ^{2}}{e ^{2} - 2}

Solution steps

\frac{( 2 x )}{( x - 1 )} = e^{2}

Simplify

\frac{( 2 x )}{( x - 1 )} : \frac{2 x}{x - 1}

\frac{2 x}{x - 1} = e^{2}

Multiply both sides by

x - 1

2 x = e^{2} (x - 1)

Expand

e^{2} (x - 1) : e^{2} x - e^{2}

2 x = e^{2} x - e^{2}

Move

e^{2} x

to the left side

2 x - e^{2} x = - e^{2}

Factor

2 x - e^{2} x : (2 - e^{2}) x

(2 - e^{2}) x = - e^{2}

Divide both sides by

2 - e^{2}

x = \frac{e ^{2}}{e ^{2} - 2}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = \frac{e ^{2}}{e ^{2} - 2}

\frac{3 x ^{2} - 6 x}{x - 2} = 0

\frac{x + 1}{2 ( 6 x - 2 )} = 6

6 = \frac{6}{x ^{2} + 2}

x, f = \frac{2 x - 1}{x}

\frac{lo g _{2} ( 8 )}{x} = 60

What is the answer to ((2x))/((x-1))=e^2 ?
The answer to ((2x))/((x-1))=e^2 is x=(e^2)/(e^2-2)