What is the answer to ((y-2))/(y+2)=e^4 ?

The answer to ((y-2))/(y+2)=e^4 is y=(2e^4+2)/(1-e^4)

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((y-2))/(y+2)=e^4

\frac{( y - 2 )}{y + 2} = e^{4}

y = \frac{2 e ^{4} + 2}{1 - e ^{4}}

Decimal Notation

y = - 2.07462 \dots

Solution steps

\frac{( y - 2 )}{y + 2} = e^{4}

Simplify

\frac{( y - 2 )}{y + 2} : \frac{y - 2}{y + 2}

\frac{y - 2}{y + 2} = e^{4}

Multiply both sides by

y + 2

y - 2 = e^{4} (y + 2)

Expand

e^{4} (y + 2) : e^{4} y + 2 e^{4}

y - 2 = e^{4} y + 2 e^{4}

Move

2

to the right side

y = e^{4} y + 2 e^{4} + 2

Move

e^{4} y

to the left side

y - e^{4} y = 2 e^{4} + 2

Factor

y - e^{4} y : (1 - e^{4}) y

(1 - e^{4}) y = 2 e^{4} + 2

Divide both sides by

1 - e^{4}

y = \frac{2 e ^{4} + 2}{1 - e ^{4}}

Verify Solutions

Find undefined (singularity) points:

y = - 2

Combine undefined points with solutions:

y = \frac{2 e ^{4} + 2}{1 - e ^{4}}

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

1 - \frac{8}{m - 5} = \frac{3}{m}

\frac{5}{x} = \frac{5}{x ^{2}}

\frac{3}{6} = \frac{7}{w}

5 - \frac{x}{2} = \frac{12}{x}

What is the answer to ((y-2))/(y+2)=e^4 ?
The answer to ((y-2))/(y+2)=e^4 is y=(2e^4+2)/(1-e^4)