What is the answer to (x+5)/x =e^3 ?

The answer to (x+5)/x =e^3 is x= 5/(e^3-1)

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(x+5)/x =e^3

\frac{x + 5}{x} = e^{3}

x = \frac{5}{e ^{3} - 1}

Decimal Notation

x = 0.26197 \dots

Solution steps

\frac{x + 5}{x} = e^{3}

Multiply both sides by

x

x + 5 = e^{3} x

Move

5

to the right side

x = e^{3} x - 5

Move

e^{3} x

to the left side

x - e^{3} x = - 5

Factor

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

(1 - e^{3}) x = - 5

Divide both sides by

1 - e^{3}

x = \frac{5}{e ^{3} - 1}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{5}{e ^{3} - 1}

\frac{3}{5 x} = 9

a (x) = \frac{3 x - 4}{2 x + 3}

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

\frac{6.57}{8} = \frac{4.57}{x}

0 = \frac{3}{x}