Solve 4/r+8/r-7

$$\frac { 4 } { r } + \frac { 8 } { r - 7 }$$

Evaluate

$$\frac{4\left(3r-7\right)}{r\left(r-7\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r and r-7 is r\left(r-7\right). Multiply \frac{4}{r} times \frac{r-7}{r-7}. Multiply \frac{8}{r-7} times \frac{r}{r}.

$$\frac{4\left(r-7\right)}{r\left(r-7\right)}+\frac{8r}{r\left(r-7\right)}$$

Since \frac{4\left(r-7\right)}{r\left(r-7\right)} and \frac{8r}{r\left(r-7\right)} have the same denominator, add them by adding their numerators.

$$\frac{4\left(r-7\right)+8r}{r\left(r-7\right)}$$

Do the multiplications in 4\left(r-7\right)+8r.

$$\frac{4r-28+8r}{r\left(r-7\right)}$$

Combine like terms in 4r-28+8r.

$$\frac{12r-28}{r\left(r-7\right)}$$

Expand r\left(r-7\right).

$$\frac{12r-28}{r^{2}-7r}$$

Factor

$$\frac{4\left(3r-7\right)}{r\left(r-7\right)}$$