What is the answer to (x+1)/x =3^{1/2} ?

The answer to (x+1)/x =3^{1/2} is x= 1/(3^{1/2)-1}

Solve for x: (x+1)/x =3^{1/2}

The solution is x= 1/(3^{1/2)-1}

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

x = \frac{1}{3 ^{\frac{1}{2}} - 1}

Decimal Notation

x = 1.36602 \dots

Solution steps

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

Multiply both sides by

x

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

Move

1

to the right side

x = 3^{\frac{1}{2}} x - 1

Move

3^{\frac{1}{2}} x

to the left side

x - 3^{\frac{1}{2}} x = - 1

Factor

x - 3^{\frac{1}{2}} x : (1 - 3^{\frac{1}{2}}) x

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

Divide both sides by

1 - 3^{\frac{1}{2}}

x = \frac{1}{3 ^{\frac{1}{2}} - 1}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{3 ^{\frac{1}{2}} - 1}

\frac{( a ) ( 7 x - 2 )}{( 4 x )} = 2

\frac{16}{x - 1} = \frac{15}{x - 1}

\frac{x ^{2} + 1}{x ^{2} - 4 ( x + \frac{1}{x} ) + 5} = 0

\frac{5 ^{2}}{x + 4 ^{2}} = 21

\frac{( x + 350 )}{x} + 315 = 92 x^{4} - 27

What is the answer to (x+1)/x =3^{1/2} ?
The answer to (x+1)/x =3^{1/2} is x= 1/(3^{1/2)-1}
Solve for x: (x+1)/x =3^{1/2}
The solution is x= 1/(3^{1/2)-1}