Simplify 5/(n+5)+(4n)/(2n+6)

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

Step 1

Cancel the common factor of $4$ and $2 n + 6$ .

Factor $2$ out of $4 n$ .

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

Cancel the common factors.

Factor $2$ out of $2 n$ .

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

Factor $2$ out of $6$ .

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

Factor $2$ out of $2 n + 2 \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

To write $\frac{5}{n + 5}$ as a fraction with a common denominator, multiply by $\frac{n + 3}{n + 3}$ .

$\frac{5}{n + 5} \cdot \frac{n + 3}{n + 3} + \frac{2 n}{n + 3}$

Step 3

To write $\frac{2 n}{n + 3}$ as a fraction with a common denominator, multiply by $\frac{n + 5}{n + 5}$ .

$\frac{5}{n + 5} \cdot \frac{n + 3}{n + 3} + \frac{2 n}{n + 3} \cdot \frac{n + 5}{n + 5}$

Step 4

Write each expression with a common denominator of $(n + 5) (n + 3)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{n + 5}$ by $\frac{n + 3}{n + 3}$ .

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

Multiply $\frac{2 n}{n + 3}$ by $\frac{n + 5}{n + 5}$ .

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

Reorder the factors of $(n + 5) (n + 3)$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Apply the distributive property.

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

Multiply $5$ by $3$ .

$\frac{5 n + 15 + 2 n (n + 5)}{(n + 3) (n + 5)}$

Apply the distributive property.

$\frac{5 n + 15 + 2 n \cdot n + 2 n \cdot 5}{(n + 3) (n + 5)}$

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

Move $n$ .

$\frac{5 n + 15 + 2 (n \cdot n) + 2 n \cdot 5}{(n + 3) (n + 5)}$

Multiply $n$ by $n$ .

$\frac{5 n + 15 + 2 n^{2} + 2 n \cdot 5}{(n + 3) (n + 5)}$

Multiply $5$ by $2$ .

$\frac{5 n + 15 + 2 n^{2} + 10 n}{(n + 3) (n + 5)}$

Add $5 n$ and $10 n$ .

$\frac{15 n + 15 + 2 n^{2}}{(n + 3) (n + 5)}$

Reorder terms.

$\frac{2 n^{2} + 15 n + 15}{(n + 3) (n + 5)}$

Simplify 5/(n+5)+(4n)/(2n+6)

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