Solve 3m/9m^2-1-1/2(3m+1)

$$\frac { 3 m } { 9 m ^ { 2 } - 1 } - \frac { 1 } { 2 ( 3 m + 1 ) }$$

Evaluate

$$\frac{1}{2\left(3m-1\right)}$$

Short Solution Steps

Factor 9m^{2}-1.

$$\frac{3m}{\left(3m-1\right)\left(3m+1\right)}-\frac{1}{2\left(3m+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(3m-1\right)\left(3m+1\right) and 2\left(3m+1\right) is 2\left(3m-1\right)\left(3m+1\right). Multiply \frac{3m}{\left(3m-1\right)\left(3m+1\right)} times \frac{2}{2}. Multiply \frac{1}{2\left(3m+1\right)} times \frac{3m-1}{3m-1}.

$$\frac{2\times 3m}{2\left(3m-1\right)\left(3m+1\right)}-\frac{3m-1}{2\left(3m-1\right)\left(3m+1\right)}$$

Since \frac{2\times 3m}{2\left(3m-1\right)\left(3m+1\right)} and \frac{3m-1}{2\left(3m-1\right)\left(3m+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3m-\left(3m-1\right)}{2\left(3m-1\right)\left(3m+1\right)}$$

Do the multiplications in 2\times 3m-\left(3m-1\right).

$$\frac{6m-3m+1}{2\left(3m-1\right)\left(3m+1\right)}$$

Combine like terms in 6m-3m+1.

$$\frac{3m+1}{2\left(3m-1\right)\left(3m+1\right)}$$

Cancel out 3m+1 in both numerator and denominator.

$$\frac{1}{2\left(3m-1\right)}$$

Expand 2\left(3m-1\right).

$$\frac{1}{6m-2}$$

Expand

$$\frac{3}{2\left(9m-3\right)}$$

Short Solution Steps

Factor 9m^{2}-1.

$$\frac{3m}{\left(3m-1\right)\left(3m+1\right)}-\frac{1}{2\left(3m+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(3m-1\right)\left(3m+1\right) and 2\left(3m+1\right) is 2\left(3m-1\right)\left(3m+1\right). Multiply \frac{3m}{\left(3m-1\right)\left(3m+1\right)} times \frac{2}{2}. Multiply \frac{1}{2\left(3m+1\right)} times \frac{3m-1}{3m-1}.

$$\frac{2\times 3m}{2\left(3m-1\right)\left(3m+1\right)}-\frac{3m-1}{2\left(3m-1\right)\left(3m+1\right)}$$

Since \frac{2\times 3m}{2\left(3m-1\right)\left(3m+1\right)} and \frac{3m-1}{2\left(3m-1\right)\left(3m+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3m-\left(3m-1\right)}{2\left(3m-1\right)\left(3m+1\right)}$$

Do the multiplications in 2\times 3m-\left(3m-1\right).

$$\frac{6m-3m+1}{2\left(3m-1\right)\left(3m+1\right)}$$

Combine like terms in 6m-3m+1.

$$\frac{3m+1}{2\left(3m-1\right)\left(3m+1\right)}$$

Cancel out 3m+1 in both numerator and denominator.

$$\frac{1}{2\left(3m-1\right)}$$

Expand 2\left(3m-1\right).

$$\frac{1}{6m-2}$$