Solve 6/r-1+6/r+1

$$\frac { 6 } { r - 1 } + \frac { 6 } { r + 1 }$$

Evaluate

$$\frac{12r}{r^{2}-1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r-1 and r+1 is \left(r-1\right)\left(r+1\right). Multiply \frac{6}{r-1} times \frac{r+1}{r+1}. Multiply \frac{6}{r+1} times \frac{r-1}{r-1}.

$$\frac{6\left(r+1\right)}{\left(r-1\right)\left(r+1\right)}+\frac{6\left(r-1\right)}{\left(r-1\right)\left(r+1\right)}$$

Since \frac{6\left(r+1\right)}{\left(r-1\right)\left(r+1\right)} and \frac{6\left(r-1\right)}{\left(r-1\right)\left(r+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{6\left(r+1\right)+6\left(r-1\right)}{\left(r-1\right)\left(r+1\right)}$$

Do the multiplications in 6\left(r+1\right)+6\left(r-1\right).

$$\frac{6r+6+6r-6}{\left(r-1\right)\left(r+1\right)}$$

Combine like terms in 6r+6+6r-6.

$$\frac{12r}{\left(r-1\right)\left(r+1\right)}$$

Expand \left(r-1\right)\left(r+1\right).

$$\frac{12r}{r^{2}-1}$$

Factor

$$\frac{12r}{r^{2}-1}$$