How do you simplify #\frac { \frac { x } { 2} - 1} { x - 2} #?

1 Answer
smendyka
Aug 7, 2017

See a solution process below:

Explanation:

First, we need to convert the numerator to a common fraction:

#(x/2 - [2/2 xx 1])/(x - 2) =>#

#(x/2 - 2/2)/(x - 2) =>#

#((x - 2)/2)/(x - 2)#

We can rewrite the expression as:

#((x - 2)/2)/((x - 2)/1)#

Next, we can use this rule of dividing fractions to simplify the expression:

#(color(red)((x - 2))/color(blue)(2))/(color(green)((x - 2))/color(purple)(1)) = (color(red)((x - 2)) xx color(purple)(1))/(color(blue)(2) xx color(green)((x - 2))) = (cancel(color(red)((x - 2))) xx color(purple)(1))/(color(blue)(2) xx cancel(color(green)((x - 2)))) = 1/2# Where:

#x - 2 !=1# or #x != 2#

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