Question

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

Answer 1

`1/2+x/3+x^2/4` with `x=1/2`
`color(white)("XXXXXXXXXXXXXXXX")=35/48`

Explanation:

Given `1/2+x/3+x^2/4` with `x=color(red)(1/2)`

`1/2+color(red)(1/2)/3+(color(red)(1/2))^2/4`

`=1/2+color(blue)((1/2)/3)+color(green)((1/4)/4)`

`=1/2+color(blue)(1/2*1/3)+color(green)((1/4)*1/4)`

`=1/2+color(blue)(1/6) + color(green)(1/16)`

least common multiple is `3xx16 = 48`

`color(blue)(1/2)+color(orange)(1/6) + color(green)(1/64)`

`=color(blue)(24/48)+color(orange)(8/48) + color(green)(35/48)`

`=35/48`