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How to solve $\frac{1}{2} + \frac{x}{3} + \frac{x^{2}}{4}$ $1/2 +x/3 +x^2/4$ where $x = \frac{1}{2}$ $x=1/2$ ? Please show steps.

1 Answer

Sep 8, 2015

$\frac{1}{2} + \frac{x}{3} + \frac{x^{2}}{4}$ $1/2+x/3+x^2/4$ with $x = \frac{1}{2}$ $x=1/2$
$XXXXXXXXXXXXXXXX = \frac{35}{48}$ $color(white)("XXXXXXXXXXXXXXXX")=35/48$

Explanation:

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

$\frac{1}{2} + \frac{\frac{1}{2}}{3} + \frac{{(\frac{1}{2})}^{2}}{4}$ $1/2+color(red)(1/2)/3+(color(red)(1/2))^2/4$

$= \frac{1}{2} + \frac{\frac{1}{2}}{3} + \frac{\frac{1}{4}}{4}$ $=1/2+color(blue)((1/2)/3)+color(green)((1/4)/4)$

$= \frac{1}{2} + \frac{1}{2} \cdot \frac{1}{3} + (\frac{1}{4}) \cdot \frac{1}{4}$ $=1/2+color(blue)(1/2*1/3)+color(green)((1/4)*1/4)$

$= \frac{1}{2} + \frac{1}{6} + \frac{1}{16}$ $=1/2+color(blue)(1/6) + color(green)(1/16)$

least common multiple is $3 \times 16 = 48$ $3xx16 = 48$

$\frac{1}{2} + \frac{1}{6} + \frac{1}{64}$ $color(blue)(1/2)+color(orange)(1/6) + color(green)(1/64)$

$= \frac{24}{48} + \frac{8}{48} + \frac{35}{48}$ $=color(blue)(24/48)+color(orange)(8/48) + color(green)(35/48)$

$= \frac{35}{48}$ $=35/48$

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