# How to solve 1/2 +x/3 +x^2/4 where x=1/2? Please show steps.

Sep 8, 2015

$\frac{1}{2} + \frac{x}{3} + {x}^{2} / 4$ with $x = \frac{1}{2}$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXXX}} = \frac{35}{48}$

#### Explanation:

Given $\frac{1}{2} + \frac{x}{3} + {x}^{2} / 4$ with $x = \textcolor{red}{\frac{1}{2}}$

$\frac{1}{2} + \frac{\textcolor{red}{\frac{1}{2}}}{3} + {\left(\textcolor{red}{\frac{1}{2}}\right)}^{2} / 4$

$= \frac{1}{2} + \textcolor{b l u e}{\frac{\frac{1}{2}}{3}} + \textcolor{g r e e n}{\frac{\frac{1}{4}}{4}}$

$= \frac{1}{2} + \textcolor{b l u e}{\frac{1}{2} \cdot \frac{1}{3}} + \textcolor{g r e e n}{\left(\frac{1}{4}\right) \cdot \frac{1}{4}}$

$= \frac{1}{2} + \textcolor{b l u e}{\frac{1}{6}} + \textcolor{g r e e n}{\frac{1}{16}}$

least common multiple is $3 \times 16 = 48$

$\textcolor{b l u e}{\frac{1}{2}} + \textcolor{\mathmr{and} a n \ge}{\frac{1}{6}} + \textcolor{g r e e n}{\frac{1}{64}}$

$= \textcolor{b l u e}{\frac{24}{48}} + \textcolor{\mathmr{and} a n \ge}{\frac{8}{48}} + \textcolor{g r e e n}{\frac{35}{48}}$

$= \frac{35}{48}$