Solve 3r/3+-r+2/6r+2

$$\frac { 3 r } { 3 } + \frac { - r + 2 } { 6 r + 2 }$$

Evaluate

$$\frac{6r^{2}+r+2}{2\left(3r+1\right)}$$

Short Solution Steps

Cancel out 3 and 3.

$$r+\frac{-r+2}{6r+2}$$

Factor 6r+2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply r times \frac{2\left(3r+1\right)}{2\left(3r+1\right)}.

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

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

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

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

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

Combine like terms in 6r^{2}+2r-r+2.

$$\frac{6r^{2}+r+2}{2\left(3r+1\right)}$$

Expand 2\left(3r+1\right).

$$\frac{6r^{2}+r+2}{6r+2}$$

Expand

$$\frac{6r^{2}+r+2}{2\left(3r+1\right)}$$

Short Solution Steps

Cancel out 3 and 3.

$$r+\frac{-r+2}{6r+2}$$

Factor 6r+2.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply r times \frac{2\left(3r+1\right)}{2\left(3r+1\right)}.

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

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

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

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

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

Combine like terms in 6r^{2}+2r-r+2.

$$\frac{6r^{2}+r+2}{2\left(3r+1\right)}$$

Expand 2\left(3r+1\right).

$$\frac{6r^{2}+r+2}{6r+2}$$