Simplify (7n)/(3n-18)+(n+3)/3

$\frac{7 n}{3 n - 18} + \frac{n + 3}{3}$

Step 1

Factor $3$ out of $3 n - 18$ .

Factor $3$ out of $3 n$ .

$\frac{7 n}{3 (n) - 18} + \frac{n + 3}{3}$

Factor $3$ out of $- 18$ .

$\frac{7 n}{3 n + 3 \cdot - 6} + \frac{n + 3}{3}$

Factor $3$ out of $3 n + 3 \cdot - 6$ .

$\frac{7 n}{3 (n - 6)} + \frac{n + 3}{3}$

Step 2

To write $\frac{n + 3}{3}$ as a fraction with a common denominator, multiply by $\frac{n - 6}{n - 6}$ .

$\frac{7 n}{3 (n - 6)} + \frac{n + 3}{3} \cdot \frac{n - 6}{n - 6}$

Step 3

Simplify terms.

Multiply $\frac{n + 3}{3}$ by $\frac{n - 6}{n - 6}$ .

$\frac{7 n}{3 (n - 6)} + \frac{(n + 3) (n - 6)}{3 (n - 6)}$

Combine the numerators over the common denominator.

$\frac{7 n + (n + 3) (n - 6)}{3 (n - 6)}$

Step 4

Simplify the numerator.

Expand $(n + 3) (n - 6)$ using the FOIL Method.

Apply the distributive property.

$\frac{7 n + n (n - 6) + 3 (n - 6)}{3 (n - 6)}$

Apply the distributive property.

$\frac{7 n + n \cdot n + n \cdot - 6 + 3 (n - 6)}{3 (n - 6)}$

Apply the distributive property.

$\frac{7 n + n \cdot n + n \cdot - 6 + 3 n + 3 \cdot - 6}{3 (n - 6)}$

Simplify and combine like terms.

Simplify each term.

Multiply $n$ by $n$ .

$\frac{7 n + n^{2} + n \cdot - 6 + 3 n + 3 \cdot - 6}{3 (n - 6)}$

Move $- 6$ to the left of $n$ .

$\frac{7 n + n^{2} - 6 \cdot n + 3 n + 3 \cdot - 6}{3 (n - 6)}$

Multiply $3$ by $- 6$ .

$\frac{7 n + n^{2} - 6 n + 3 n - 18}{3 (n - 6)}$

Add $- 6 n$ and $3 n$ .

$\frac{7 n + n^{2} - 3 n - 18}{3 (n - 6)}$

Subtract $3 n$ from $7 n$ .

$\frac{n^{2} + 4 n - 18}{3 (n - 6)}$