What is the answer to x/((x-1))+((x-1))/x = 21/2 ?

The answer to x/((x-1))+((x-1))/x = 21/2 is x=-(-sqrt(17)+5)/(2sqrt(17)),x=(sqrt(17)+5)/(2sqrt(17))

Solve for x: x/((x-1))+((x-1))/x = 21/2

The solution is x=-(-sqrt(17)+5)/(2sqrt(17)),x=(sqrt(17)+5)/(2sqrt(17))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{x}{( x - 1 )} + \frac{( x - 1 )}{x} = \frac{21}{2}

x = - \frac{- 17 + 5}{2 17}, x = \frac{17 + 5}{2 17}

Decimal Notation

x = - 0.10633 \dots, x = 1.10633 \dots

Solution steps

\frac{x}{( x - 1 )} + \frac{( x - 1 )}{x} = \frac{21}{2}

Multiply by LCM

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

Solve

2 x^{2} + 2 (x - 1)^{2} = 21 x (x - 1) : x = - \frac{- 17 + 5}{2 17}, x = \frac{17 + 5}{2 17}

x = - \frac{- 17 + 5}{2 17}, x = \frac{17 + 5}{2 17}

Verify Solutions

Find undefined (singularity) points:

x = 1, x = 0

Combine undefined points with solutions:

x = - \frac{- 17 + 5}{2 17}, x = \frac{17 + 5}{2 17}

\frac{2}{( x - 3 )} + \frac{1}{( x - 1 )} = \frac{5}{( x - 1 )} - \frac{2}{( x - 2 )}

\frac{1}{7 \cdot x ^{2} + 1} = \frac{4}{7 \cdot x}

x, 3 y = \frac{( 7 w )}{x}

\frac{7 x - 3 + 32}{3 \cdot x - 1} = \frac{1}{3}

\frac{2.5 x + 2}{5} = \frac{4}{5 - 3.5 x}

What is the answer to x/((x-1))+((x-1))/x = 21/2 ?
The answer to x/((x-1))+((x-1))/x = 21/2 is x=-(-sqrt(17)+5)/(2sqrt(17)),x=(sqrt(17)+5)/(2sqrt(17))
Solve for x: x/((x-1))+((x-1))/x = 21/2
The solution is x=-(-sqrt(17)+5)/(2sqrt(17)),x=(sqrt(17)+5)/(2sqrt(17))