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

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

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x/(x+1)=e^2

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

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

Decimal Notation

x = - 1.15651 \dots

Solution steps

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

Multiply both sides by

x + 1

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

Expand

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

x = e^{2} x + e^{2}

Move

e^{2} x

to the left side

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

Factor

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

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

Divide both sides by

1 - e^{2}

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

Verify Solutions

Find undefined (singularity) points:

x = - 1

Combine undefined points with solutions:

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

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

\frac{4}{2 x + 1} + \frac{1}{4 x ^{2} - 1} = 3

\frac{1}{x ^{2} - 8 x} + \frac{6 x}{x - 8} = - 1

\frac{1}{x} + \frac{1}{x + 5} = \frac{1}{6}

\frac{600}{300 + x} = \frac{400}{300 - x}

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