What is the answer to (4110+x)/x =e^{0.45pi} ?

The answer to (4110+x)/x =e^{0.45pi} is x=(4110)/(e^{0.45pi)-1}

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(4110+x)/x =e^{0.45pi}

\frac{4110 + x}{x} = e^{0.45 π}

x = \frac{4110}{e ^{0.45 π} - 1}

Decimal Notation

x = 1321.03065 \dots

Solution steps

\frac{4110 + x}{x} = e^{0.45 π}

Multiply both sides by

x

4110 + x = e^{0.45 π} x

Move

4110

to the right side

x = e^{0.45 π} x - 4110

Move

e^{0.45 π} x

to the left side

x - e^{0.45 π} x = - 4110

Factor

x - e^{0.45 π} x : (1 - e^{0.45 π}) x

(1 - e^{0.45 π}) x = - 4110

Divide both sides by

1 - e^{0.45 π}

x = \frac{4110}{e ^{0.45 π} - 1}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{4110}{e ^{0.45 π} - 1}

1 + \frac{5}{x} = - \frac{4}{x ^{2}}

\frac{1080}{100} = \frac{944}{x}

\frac{x}{( 1 - x ) ^{2}} = 9.6

x^{2} + 3 x - \frac{20}{x ^{2} + 3 x} = 8

\frac{38}{x} = 0.29

What is the answer to (4110+x)/x =e^{0.45pi} ?
The answer to (4110+x)/x =e^{0.45pi} is x=(4110)/(e^{0.45pi)-1}