What is the answer to 1/100 =(x/((1-x)))^2 ?

The answer to 1/100 =(x/((1-x)))^2 is x=-1/9 ,x= 1/11

Solve for x: 1/100 =(x/((1-x)))^2

The solution is x=-1/9 ,x= 1/11

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\frac{1}{100} = (\frac{x}{( 1 - x )})^{2}

x = - \frac{1}{9}, x = \frac{1}{11}

Decimal Notation

x = - 0.11111 \dots, x = 0.09090 \dots

Solution steps

\frac{1}{100} = (\frac{x}{( 1 - x )})^{2}

Cross multiply

(1 - x)^{2} = 100 x^{2}

Solve

(1 - x)^{2} = 100 x^{2} : x = - \frac{1}{9}, x = \frac{1}{11}

x = - \frac{1}{9}, x = \frac{1}{11}

Verify Solutions

Find undefined (singularity) points:

x = 1

Combine undefined points with solutions:

x = - \frac{1}{9}, x = \frac{1}{11}

\frac{31}{2 - 4 ( 2 x - 3 )} = \frac{1}{3 \cdot ( \frac{3}{4} - 6 x )}

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

\frac{x}{( x + 1 )} + \frac{( x + 1 )}{x} = \frac{21}{12}

\frac{2}{5} = \frac{2.4}{b}

\frac{7}{x + 2} = \frac{3}{x - 5}

What is the answer to 1/100 =(x/((1-x)))^2 ?
The answer to 1/100 =(x/((1-x)))^2 is x=-1/9 ,x= 1/11
Solve for x: 1/100 =(x/((1-x)))^2
The solution is x=-1/9 ,x= 1/11