What is the answer to sqrt(x/(1-x))+sqrt((1-x)/x)=2 1/6 ?

The answer to sqrt(x/(1-x))+sqrt((1-x)/x)=2 1/6 is x\approx 0.30769…,x\approx 0.69230…

Solve for x: sqrt(x/(1-x))+sqrt((1-x)/x)=2 1/6

The solution is x\approx 0.30769…,x\approx 0.69230…

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\frac{x}{1 - x} + \frac{1 - x}{x} = 2 \frac{1}{6}

x \approx 0.30769 \dots, x \approx 0.69230 \dots

Solution steps

\frac{x}{1 - x} + \frac{1 - x}{x} = 2 \frac{1}{6}

Convert mixed numbers to improper fractions:

2 \frac{1}{6} = \frac{13}{6}

\frac{x}{1 - x} + \frac{1 - x}{x} = \frac{13}{6}

Multiply both sides by

6

\frac{x}{1 - x} \cdot 6 + \frac{1 - x}{x} \cdot 6 = \frac{13}{6} \cdot 6

Simplify

\frac{x}{1 - x} \cdot 6 + \frac{1 - x}{x} \cdot 6 = 13

Remove square roots

\frac{24336 x ^{3} - 31320 x ^{2} + 6984 x + 1296}{x ^{4} - 2 x ^{3} + x ^{2}} + 28561 = \frac{24336 ( 1 - x )}{x}

Solve

\frac{24336 x ^{3} - 31320 x ^{2} + 6984 x + 1296}{x ^{4} - 2 x ^{3} + x ^{2}} + 28561 = \frac{24336 ( 1 - x )}{x} : x \approx 0.13259 \dots, x \approx 0.30769 \dots, x \approx 0.69230 \dots, x \approx 0.86740 \dots

x \approx 0.13259 \dots, x \approx 0.30769 \dots, x \approx 0.69230 \dots, x \approx 0.86740 \dots

Verify Solutions:

x \approx 0.13259 \dots

False

, x \approx 0.30769 \dots

True

, x \approx 0.69230 \dots

True

, x \approx 0.86740 \dots

False

The solutions are

x \approx 0.30769 \dots, x \approx 0.69230 \dots

3 \cdot x^{2} + 2 x - 3 = 0

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

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

x, x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4

4 \cdot (x + 5)^{2} = 6

What is the answer to sqrt(x/(1-x))+sqrt((1-x)/x)=2 1/6 ?
The answer to sqrt(x/(1-x))+sqrt((1-x)/x)=2 1/6 is x\approx 0.30769…,x\approx 0.69230…
Solve for x: sqrt(x/(1-x))+sqrt((1-x)/x)=2 1/6
The solution is x\approx 0.30769…,x\approx 0.69230…