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

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

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((x+5)/x)=3e

(\frac{x + 5}{x}) = 3 e

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

Decimal Notation

x = 0.69882 \dots

Solution steps

(\frac{x + 5}{x}) = 3 e

Simplify

(\frac{x + 5}{x}) : \frac{x + 5}{x}

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

Multiply both sides by

x

x + 5 = 3 e x

Move

5

to the right side

x = 3 e x - 5

Move

3 e x

to the left side

x - 3 e x = - 5

Factor

x - 3 e x : (1 - 3 e) x

(1 - 3 e) x = - 5

Divide both sides by

1 - 3 e

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

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

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

\frac{x ^{2} + 5 x + 2}{x + 2} = 3

\frac{12}{b} - 3 = \frac{6}{b} + 4

28 = \frac{2100 - x}{x} 100

\frac{1}{2 x + \frac{3}{2} x} = 4044

\frac{3492}{x} = 3.88