# How do you write the mixed expression (x+7)/(2x)-5x as a rational expression?

Nov 23, 2017

$\frac{- 10 {x}^{2} + x + 7}{2 x}$

#### Explanation:

Multiply by 1 and you do not change the value. However, 1 comes in many forms

Note that $5 x \text{ is also } \frac{5 x}{1}$

$\textcolor{g r e e n}{\left[\frac{x + 7}{2 x}\right] - \left[\frac{5 x}{1} \textcolor{red}{\times 1}\right]}$

$\textcolor{g r e e n}{\left[\frac{x + 7}{2 x}\right] - \left[\frac{5 x}{1} \textcolor{red}{\times \frac{2 x}{2 x}}\right]}$

$\textcolor{g r e e n}{\left[\frac{x + 7}{2 x}\right] - \left[\frac{5 x \textcolor{red}{\times 2 x}}{\textcolor{red}{2 x}}\right]}$

color(green)([(x+7)/(2x)]-[(10x^2)/(2x)]

$\textcolor{g r e e n}{\frac{- 10 {x}^{2} + x + 7}{2 x}}$