What is the answer to ((3/((x-1)))+4)/x =2 ?

The answer to ((3/((x-1)))+4)/x =2 is x=(3+sqrt(7))/2 ,x=(3-sqrt(7))/2

Solve for x: ((3/((x-1)))+4)/x =2

The solution is x=(3+sqrt(7))/2 ,x=(3-sqrt(7))/2

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\frac{( \frac{3}{( x - 1 )} ) + 4}{x} = 2

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

Decimal Notation

x = 2.82287 \dots, x = 0.17712 \dots

Solution steps

\frac{( \frac{3}{( x - 1 )} ) + 4}{x} = 2

Simplify

\frac{( \frac{3}{x - 1} ) + 4}{x} : \frac{4 x - 1}{x ( x - 1 )}

\frac{4 x - 1}{x ( x - 1 )} = 2

Multiply both sides by

x (x - 1)

4 x - 1 = 2 x (x - 1)

Solve

4 x - 1 = 2 x (x - 1) : x = \frac{3 + 7}{2}, x = \frac{3 - 7}{2}

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

Verify Solutions

Find undefined (singularity) points:

x = 0, x = 1

Combine undefined points with solutions:

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

\frac{x}{23 x} = (16 mod 107)

x, \frac{2}{x} + 2 y + \frac{1}{2} x - y + \frac{5}{9} = 0

\frac{( x + 4 )}{( x + 2 )} = 3

\frac{y ^{2} - 5}{3 y} = \frac{- 1}{3}

\frac{13 y ^{2} + 12}{y ^{2}} = 44

What is the answer to ((3/((x-1)))+4)/x =2 ?
The answer to ((3/((x-1)))+4)/x =2 is x=(3+sqrt(7))/2 ,x=(3-sqrt(7))/2
Solve for x: ((3/((x-1)))+4)/x =2
The solution is x=(3+sqrt(7))/2 ,x=(3-sqrt(7))/2