What is the answer to (2x}{x+1}=\frac{2x+1)/x ?

The answer to (2x}{x+1}=\frac{2x+1)/x is x=-1/3

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

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

x = - \frac{1}{3}

Solution steps

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

Cross multiply

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

Subtract

2 x^{2} + 3 x

from both sides

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

Simplify

- 3 x = 1

Divide both sides by

- 3

x = - \frac{1}{3}

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 0

Combine undefined points with solutions:

x = - \frac{1}{3}

\frac{8 h}{3 j} = 6 k

\frac{n !}{( n - 2 ) !} = 20

\frac{x ^{2} - 2 x - 3}{( x - 3 ) ^{2}} = 0

\frac{a x + b}{c x + d} = 2, x

\frac{4}{z} = \frac{3 z}{z - 3}

What is the answer to (2x}{x+1}=\frac{2x+1)/x ?
The answer to (2x}{x+1}=\frac{2x+1)/x is x=-1/3
Solve for x: (2x}{x+1}=\frac{2x+1)/x
The solution is x=-1/3