Simplify 1/(2x+1)+5

$\frac{1}{2 x + 1} + 5$

Step 1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2 x + 1}{2 x + 1}$ .

$\frac{1}{2 x + 1} + \frac{5 (2 x + 1)}{2 x + 1}$

Step 2

Combine the numerators over the common denominator.

$\frac{1 + 5 (2 x + 1)}{2 x + 1}$

Step 3

Simplify the numerator.

Apply the distributive property.

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

Multiply $2$ by $5$ .

$\frac{1 + 10 x + 5 \cdot 1}{2 x + 1}$

Multiply $5$ by $1$ .

$\frac{1 + 10 x + 5}{2 x + 1}$

Add $1$ and $5$ .

$\frac{10 x + 6}{2 x + 1}$

Factor $2$ out of $10 x + 6$ .

Factor $2$ out of $10 x$ .

$\frac{2 (5 x) + 6}{2 x + 1}$

Factor $2$ out of $6$ .

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

Factor $2$ out of $2 (5 x) + 2 (3)$ .

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