Simplify 5/(2n^2-2n)+(3n)/3

$\frac{5}{2 n^{2} - 2 n} + \frac{3 n}{3}$

Simplify each term.

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

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

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

Factor $2 n$ out of $- 2 n$ .

$\frac{5}{2 n (n) + 2 n (- 1)} + \frac{3 n}{3}$

Factor $2 n$ out of $2 n (n) + 2 n (- 1)$ .

$\frac{5}{2 n (n - 1)} + \frac{3 n}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5}{2 n (n - 1)} + \frac{3 n}{3}$

Divide $n$ by $1$ .

$\frac{5}{2 n (n - 1)} + n$

To write $n$ as a fraction with a common denominator, multiply by $\frac{2 n (n - 1)}{2 n (n - 1)}$ .

$\frac{5}{2 n (n - 1)} + n \cdot \frac{2 n (n - 1)}{2 n (n - 1)}$

Simplify terms.

Combine $n$ and $\frac{2 n (n - 1)}{2 n (n - 1)}$ .

$\frac{5}{2 n (n - 1)} + \frac{n (2 n (n - 1))}{2 n (n - 1)}$

Combine the numerators over the common denominator.

$\frac{5 + n (2 n (n - 1))}{2 n (n - 1)}$

Simplify the numerator.

Rewrite using the commutative property of multiplication.

$\frac{5 + 2 n (n (n - 1))}{2 n (n - 1)}$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$\frac{5 + 2 (n \cdot n) (n - 1)}{2 n (n - 1)}$

Multiply $n$ by $n$ .

$\frac{5 + 2 n^{2} (n - 1)}{2 n (n - 1)}$

Apply the distributive property.

$\frac{5 + 2 n^{2} n + 2 n^{2} \cdot - 1}{2 n (n - 1)}$

Multiply $n^{2}$ by $n$ by adding the exponents.

Move $n$ .

$\frac{5 + 2 (n \cdot n^{2}) + 2 n^{2} \cdot - 1}{2 n (n - 1)}$

Multiply $n$ by $n^{2}$ .

Raise $n$ to the power of $1$ .

$\frac{5 + 2 (n^{1} n^{2}) + 2 n^{2} \cdot - 1}{2 n (n - 1)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 + 2 n^{1 + 2} + 2 n^{2} \cdot - 1}{2 n (n - 1)}$

Add $1$ and $2$ .

$\frac{5 + 2 n^{3} + 2 n^{2} \cdot - 1}{2 n (n - 1)}$

Multiply $- 1$ by $2$ .

$\frac{5 + 2 n^{3} - 2 n^{2}}{2 n (n - 1)}$

Reorder terms.

$\frac{2 n^{3} - 2 n^{2} + 5}{2 n (n - 1)}$