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

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

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

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

x = 2, x = - 2

Solution steps

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

Convert mixed numbers to improper fractions:

2 \frac{2}{3} = \frac{8}{3}

\frac{x}{x - 1} + \frac{x}{x + 1} = \frac{8}{3}

Multiply by LCM

3 x (x + 1) + 3 x (x - 1) = 8 (x - 1) (x + 1)

Solve

3 x (x + 1) + 3 x (x - 1) = 8 (x - 1) (x + 1) : x = 2, x = - 2

x = 2, x = - 2

Verify Solutions

Find undefined (singularity) points:

x = 1, x = - 1

Combine undefined points with solutions:

x = 2, x = - 2

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

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

7 - \frac{1}{x} = - 8 x

\frac{3 a}{2 a + 1} - \frac{4}{2 a - 1} = 1

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

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