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

The answer to ((x+1)/x)^2=2((x+1)/x)+3 is x= 1/2 ,x=-1/2

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((x+1)/x)^2=2((x+1)/x)+3

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

x = \frac{1}{2}, x = - \frac{1}{2}

Decimal Notation

x = 0.5, x = - 0.5

Solution steps

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

Multiply by LCM

(x + 1)^{2} = 2 x (x + 1) + 3 x^{2}

Solve

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

x = \frac{1}{2}, x = - \frac{1}{2}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = \frac{1}{2}, x = - \frac{1}{2}

\frac{( x - \frac{1}{3} ) ^{2} + 2}{3 \cdot x} = \frac{10}{9}

\frac{( x ^{2} - 6 )}{x} - \frac{( 3 x )}{( x ^{2} - 6 )} = - 2

\frac{( 3 x + 7 )}{( x + 2 ) + x} = \frac{1}{( x + 2 ) + 8}

\frac{( x + 1 )}{3} = \frac{21}{2 + 2 x - 1}

a, (a + b)^{- 1} = a^{- 1} + b^{- 1}

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