How do you evaluate #\frac { 4x - 12} { 4} \div \frac { 2x - 6} { 6}#?

1 Answer
smendyka
Nov 20, 2017

See a solution process below:

Explanation:

First, factor the numerator of the left fraction as:

#(2(2x - 6))/4 -: (2x - 6)/6#

Next, rewrite the expression as:

#((2(2x - 6))/4)/((2x - 6)/6)#

Now, use this rule for dividing fractions to complete the evaluation of the expression:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

#(color(red)(2(2x - 6))/color(blue)(4))/(color(green)(2x - 6)/color(purple)(6)) =>#

#(color(red)(2(2x - 6)) xx color(purple)(6))/(color(blue)(4) xx color(green)((2x - 6))) =>#

#(color(red)(2(2x - 6)) xx color(purple)((2 xx 3)))/(color(blue)((2 xx 2) xx color(green)((2x - 6)))) =>#

#(color(red)(color(blue)(cancel(color(red)(2)))color(green)(cancel(color(red)((2x - 6))))) xx color(purple)((color(blue)(cancel(color(purple)(2))) xx 3)))/(color(blue)((color(red)(cancel(color(blue)(2))) xx color(purple)(cancel(color(blue)(2)))) xx color(green)(color(red)(cancel(color(green)((2x - 6))))))) =>#

#3#

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