Simplify (4n)/(6n^2+24n)+(6n)/(6n^2+24n)

$\frac{4 n}{6 n^{2} + 24 n} + \frac{6 n}{6 n^{2} + 24 n}$

Step 1

Combine the numerators over the common denominator.

$\frac{4 n + 6 n}{6 n^{2} + 24 n}$

Step 2

Add $4 n$ and $6 n$ .

$\frac{10 n}{6 n^{2} + 24 n}$

Step 3

Factor $6 n$ out of $6 n^{2} + 24 n$ .

Factor $6 n$ out of $6 n^{2}$ .

$\frac{10 n}{6 n (n) + 24 n}$

Factor $6 n$ out of $24 n$ .

$\frac{10 n}{6 n (n) + 6 n (4)}$

Factor $6 n$ out of $6 n (n) + 6 n (4)$ .

$\frac{10 n}{6 n (n + 4)}$

Step 4

Cancel the common factor of $10$ and $6$ .

Factor $2$ out of $10 n$ .

$\frac{2 (5 n)}{6 n (n + 4)}$

Cancel the common factors.

Factor $2$ out of $6 n (n + 4)$ .

$\frac{2 (5 n)}{2 (3 n (n + 4))}$

Cancel the common factor.

$\frac{2 (5 n)}{2 (3 n (n + 4))}$

Rewrite the expression.

$\frac{5 n}{3 n (n + 4)}$

Step 5

Cancel the common factor of $n$ .

Cancel the common factor.

$\frac{5 n}{3 n (n + 4)}$

Rewrite the expression.

$\frac{5}{3 (n + 4)}$