How do you simplify #\frac { \frac { x } { 2} + \frac { x } { 3} } { \frac { x } { 4} }#?

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Answer 1 · 2016-11-08T15:59:04

Method of first principles given in detail so you can what is happening.

#3 1/3#

This is the same as: #(x/2+x/3)-:x/4#

Which is the same as:#(x/2+x/3)xx4/x#

Multiply everything inside the brackets by #4/x# giving:

#[(cancel(x))/2xx4/(cancel(x))]" "+" " [(cancel(x))/3xx4/(cancel(x))]#

#=4/2+4/3#

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way it looks without changing the actual value.

#color(green)([4/2color(magenta)(xx1)]+[4/3color(magenta)(xx1)])#

Is the same as:

#color(green)([4/2color(magenta)(xx3/3)]+[4/3color(magenta)(xx2/2)])#

#12/6+8/6" "=" "20/6#

#(20-:2)/(6-:2) = 10/3 = 3 1/3#