Solve 5r+3/r+4-8/7

$$\frac { 5 r + 3 } { r + 4 } - \frac { 8 } { 7 }$$

Evaluate

$$\frac{27r-11}{7\left(r+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r+4 and 7 is 7\left(r+4\right). Multiply \frac{5r+3}{r+4} times \frac{7}{7}. Multiply \frac{8}{7} times \frac{r+4}{r+4}.

$$\frac{7\left(5r+3\right)}{7\left(r+4\right)}-\frac{8\left(r+4\right)}{7\left(r+4\right)}$$

Since \frac{7\left(5r+3\right)}{7\left(r+4\right)} and \frac{8\left(r+4\right)}{7\left(r+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\left(5r+3\right)-8\left(r+4\right)}{7\left(r+4\right)}$$

Do the multiplications in 7\left(5r+3\right)-8\left(r+4\right).

$$\frac{35r+21-8r-32}{7\left(r+4\right)}$$

Combine like terms in 35r+21-8r-32.

$$\frac{27r-11}{7\left(r+4\right)}$$

Expand 7\left(r+4\right).

$$\frac{27r-11}{7r+28}$$

Expand

$$\frac{27r-11}{7\left(r+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of r+4 and 7 is 7\left(r+4\right). Multiply \frac{5r+3}{r+4} times \frac{7}{7}. Multiply \frac{8}{7} times \frac{r+4}{r+4}.

$$\frac{7\left(5r+3\right)}{7\left(r+4\right)}-\frac{8\left(r+4\right)}{7\left(r+4\right)}$$

Since \frac{7\left(5r+3\right)}{7\left(r+4\right)} and \frac{8\left(r+4\right)}{7\left(r+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7\left(5r+3\right)-8\left(r+4\right)}{7\left(r+4\right)}$$

Do the multiplications in 7\left(5r+3\right)-8\left(r+4\right).

$$\frac{35r+21-8r-32}{7\left(r+4\right)}$$

Combine like terms in 35r+21-8r-32.

$$\frac{27r-11}{7\left(r+4\right)}$$

Expand 7\left(r+4\right).

$$\frac{27r-11}{7r+28}$$