What is the answer to ((x+8))/x =e^3 ?

The answer to ((x+8))/x =e^3 is x= 8/(e^3-1)

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((x+8))/x =e^3

\frac{( x + 8 )}{x} = e^{3}

x = \frac{8}{e ^{3} - 1}

Decimal Notation

x = 0.41916 \dots

Solution steps

\frac{( x + 8 )}{x} = e^{3}

Simplify

\frac{( x + 8 )}{x} : \frac{x + 8}{x}

\frac{x + 8}{x} = e^{3}

Multiply both sides by

x

x + 8 = e^{3} x

Move

8

to the right side

x = e^{3} x - 8

Move

e^{3} x

to the left side

x - e^{3} x = - 8

Factor

x - e^{3} x : (1 - e^{3}) x

(1 - e^{3}) x = - 8

Divide both sides by

1 - e^{3}

x = \frac{8}{e ^{3} - 1}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{8}{e ^{3} - 1}

\frac{1.5}{3} = \frac{1}{x}

a, \frac{a}{b} + c + \frac{b}{c} + a + \frac{c}{a} + b = 0

\frac{( x - 1 )}{( x + 1 )} + \frac{( x + 1 )}{( x - 1 )} = \frac{5}{2}

\frac{( x - 5 )}{( x + 3 ) - 1} = \frac{( 5 x - 2 )}{( 9 - x ^{2} )}

x, \frac{3}{x} + \frac{3}{y} = 6

What is the answer to ((x+8))/x =e^3 ?
The answer to ((x+8))/x =e^3 is x= 8/(e^3-1)