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

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

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

\frac{x}{x - 1} + \frac{2 x}{x + 1} = 3

x = 3

Solution steps

\frac{x}{x - 1} + \frac{2 x}{x + 1} = 3

Multiply by LCM

x (x + 1) + 2 x (x - 1) = 3 (x - 1) (x + 1)

Expand

(x - 1) (x + 1) : x^{2} - 1

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

Expand

3 (x^{2} - 1) : 3 x^{2} - 3

3 x^{2} - x = 3 x^{2} - 3

Expand

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

3 x^{2} - x = 3 x^{2} - 3

Move

3 x^{2}

to the left side

- x = - 3

Divide both sides by

- 1

x = 3

Verify Solutions

Find undefined (singularity) points:

x = 1, x = - 1

Combine undefined points with solutions:

x = 3

\frac{x ^{k + 1}}{x} = x^{k}

\frac{2 x - 5}{x} = \frac{11}{3}

- 1 - \frac{7}{x} = - 6 x

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

\frac{28}{x} = \frac{24}{x - 12}

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