How do you solve #\frac { u } { 3} - \frac { 5} { 12} = \frac { u } { 4}#?

1 Answer
smendyka
Apr 7, 2017

See the entire solution process below:

Explanation:

First, multiply each side of the equation by #color(red)(12)# to eliminate the fractions while keeping the equation balanced. #color(red)(12)# is the Lowest Common Denominator of the three fractions:

#color(red)(12)(u/3 - 5/12) = color(red)(12) xx u/4#

#(color(red)(12) xx u/3) - (color(red)(12) xx 5/12) = cancel(color(red)(12))3 xx u/color(red)(cancel(color(black)(4)))#

#(cancel(color(red)(12))4 xx u/color(red)(cancel(color(black)(3)))) - (cancel(color(red)(12)) xx 5/color(red)(cancel(color(black)(12)))) = 3u#

#4u - 5 = 3u#

Now, add #color(red)(5)# and subtract #color(blue)(3u)# from each side of the equation to solve for #u# while keeping the equation balanced:

#4u - 5 + color(red)(5) - color(blue)(3u) = 3u + color(red)(5) - color(blue)(3u)#

#4u - color(blue)(3u) - 5 + color(red)(5) = 3u - color(blue)(3u) + color(red)(5)#

#(4 - color(blue)(3))u - 0 = 0 + 5#

#1u = 5#

#u = 5#

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