What is the answer to x/((1-x))+((1-x))/x = 21/6 ?

The answer to x/((1-x))+((1-x))/x = 21/6 is x=(11+sqrt(33))/(22),x=(11-sqrt(33))/(22)

Solve for x: x/((1-x))+((1-x))/x = 21/6

The solution is x=(11+sqrt(33))/(22),x=(11-sqrt(33))/(22)

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\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}

x = \frac{11 + 33}{22}, x = \frac{11 - 33}{22}

Decimal Notation

x = 0.76111 \dots, x = 0.23888 \dots

Solution steps

\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}

Multiply by LCM

6 x^{2} + 6 (1 - x)^{2} = 21 x (- x + 1)

Solve

6 x^{2} + 6 (1 - x)^{2} = 21 x (- x + 1) : x = \frac{11 + 33}{22}, x = \frac{11 - 33}{22}

x = \frac{11 + 33}{22}, x = \frac{11 - 33}{22}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = \frac{11 + 33}{22}, x = \frac{11 - 33}{22}

\frac{24}{3 a} = 4

y, x = \frac{28}{y}

0.1 = \frac{0.09}{y}

\frac{0 \cdot 25}{x} = 25

x^{2} + x + x^{- 1} + x^{- 2} = 4

What is the answer to x/((1-x))+((1-x))/x = 21/6 ?
The answer to x/((1-x))+((1-x))/x = 21/6 is x=(11+sqrt(33))/(22),x=(11-sqrt(33))/(22)
Solve for x: x/((1-x))+((1-x))/x = 21/6
The solution is x=(11+sqrt(33))/(22),x=(11-sqrt(33))/(22)