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

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

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(3x)/(x^2-1)= x/(x+1)-4

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

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

Decimal

x = - 2, x = 0.66666 \dots

Solution steps

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

Multiply by LCM

3 x = x (x - 1) - 4 (x + 1) (x - 1)

Solve

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

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

Verify Solutions

Find undefined (singularity) points:

x = - 1, x = 1

Combine undefined points with solutions:

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

1 - \frac{2}{( x - 1 ) ^{2}} = 0

\frac{18}{x ^{3}} = 0

\frac{x ^{2} - 19 x + 84}{x ^{2} - 16 x + 48} = 0

\frac{14}{15} = \frac{26}{x}

\frac{1}{x ^{2}} - \frac{1}{x} = 0

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