How do you simplify #(1-(3/x) )/ ((x/12)-(1/4))#?

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Answer 1 · 2015-10-17T00:24:23

#12/x#

Your starting expression looks like this

#(1 - 3/x)/(x/12 - 1/4)#

Start by focusing on the numerator

#1 - 3/x#

which can be rewritten as

#1 - 3/x = 1 * x/x - 3/x = (x-3)/x#

The denominator can be written as

#x/12 - 1/4 = x/12 - 1/4 * 3/3 = (x-3)/12#

You know that you can write

#color(blue)(a/b = a * 1/b " , "b != 0)#

which means that you have

#color(red)(cancel(color(black)(x-3)))/x * 12/color(red)(cancel(color(black)(x-3))) = color(green)(12/x)#