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

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

Solve for m: (3m+1)/(3m-1)-(3m-1)/(3m+1)=2

The solution is m=(1+sqrt(2))/3 ,m=(1-sqrt(2))/3

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

m = \frac{1 + 2}{3}, m = \frac{1 - 2}{3}

Decimal

m = 0.80473 \dots, m = - 0.13807 \dots

Solution steps

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

Multiply by LCM

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

Solve

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

m = \frac{1 + 2}{3}, m = \frac{1 - 2}{3}

Verify Solutions

Find undefined (singularity) points:

m = \frac{1}{3}, m = - \frac{1}{3}

Combine undefined points with solutions:

m = \frac{1 + 2}{3}, m = \frac{1 - 2}{3}

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

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

\frac{12}{x} - \frac{22}{x - 4} + 4 = 0

\frac{3}{3 x + 2} = \frac{6}{5 x}

x - \frac{x + 5}{x + 6} = \frac{1}{x + 6}

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