# How do you simplify (2x) /( x + 4) + (x + 1)/ (2x )?

Apr 26, 2017

color(blue)((5x^2+5x+4)/(2x(x+4))

#### Explanation:

$\frac{2 x}{x + 4} + \frac{x + 1}{2 x}$

$\therefore = \frac{2 x \times 2 x + \left(x + 4\right) \times \left(x + 1\right)}{2 x \left(x + 4\right)}$

$\therefore = \frac{4 {x}^{2} + {x}^{2} + 5 x + 4}{2 x \left(x + 4\right)}$

:.color(blue)(=(5x^2+5x+4)/(2x(x+4))