What is the answer to sqrt(x/((1+x)))+sqrt(((1+x))/x)= 5/2 ?

The answer to sqrt(x/((1+x)))+sqrt(((1+x))/x)= 5/2 is x= 1/3 ,x=-4/3

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sqrt(x/((1+x)))+sqrt(((1+x))/x)= 5/2

\frac{x}{( 1 + x )} + \frac{( 1 + x )}{x} = \frac{5}{2}

x = \frac{1}{3}, x = - \frac{4}{3}

Solution steps

\frac{x}{( 1 + x )} + \frac{( 1 + x )}{x} = \frac{5}{2}

Multiply both sides by

2

\frac{x}{1 + x} \cdot 2 + \frac{1 + x}{x} \cdot 2 = \frac{5}{2} \cdot 2

Simplify

\frac{x}{1 + x} \cdot 2 + \frac{1 + x}{x} \cdot 2 = 5

Remove square roots

\frac{400 x ^{3} + 664 x ^{2} + 264 x + 16}{x ^{4} + 2 x ^{3} + x ^{2}} + 625 = \frac{400 ( 1 + x )}{x}

Solve

\frac{400 x ^{3} + 664 x ^{2} + 264 x + 16}{x ^{4} + 2 x ^{3} + x ^{2}} + 625 = \frac{400 ( 1 + x )}{x} : x = \frac{1}{3}, x = - \frac{4}{3}, x = \frac{- 5 + 41}{10}, x = - \frac{5 + 41}{10}

x = \frac{1}{3}, x = - \frac{4}{3}, x = \frac{- 5 + 41}{10}, x = - \frac{5 + 41}{10}

Verify Solutions:

x = \frac{1}{3}

True

, x = - \frac{4}{3}

True

, x = \frac{- 5 + 41}{10}

False

, x = - \frac{5 + 41}{10}

False

The solutions are

x = \frac{1}{3}, x = - \frac{4}{3}

36 = x^{\frac{2}{3}}

\frac{x}{3} = 15

x - 1 = 12

6 y - 5 y + 1 = 0

2 x + 1 + 3 x + 4 = 7

What is the answer to sqrt(x/((1+x)))+sqrt(((1+x))/x)= 5/2 ?
The answer to sqrt(x/((1+x)))+sqrt(((1+x))/x)= 5/2 is x= 1/3 ,x=-4/3
Solve for x: sqrt(x/((1+x)))+sqrt(((1+x))/x)= 5/2
The solution is x= 1/3 ,x=-4/3