How do you simplify #(x-2)/2 - x/6 + -2 #?

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Answer 1 · 2016-12-23T13:42:57

#(x - 9)/3#

To simplify this expression we need to add the fractions.

To add fractions we need to get each fraction over a common denominator, in this case #color(red)(6)#

To get each term over a common denominator we must multiply the fraction by the correct form of #1#:

#(color(blue)(3/3) xx (x - 2)/2) - x/6 + (color(green)(6/6) xx -2)#

#(color(blue)(3) xx (x - 2))/(color(blue)(3) xx 2) - x/6 + (color(green)(6) xx -2)/color(green)(6)#

#(3x - 6)/6 - x/6 + -12/6#

#(3x - 6)/6 - x/6 - 12/6#

We can now add the numerators to give:

#(3x - 6 - x - 12)/6#

Next we can group like terms in the numerator:

#(3x - x - 6 - 12)/6#

Then we can combine like terms in the numerator:

#((3 - 1)x - 18)/6#

#(2x - 18)/6#

Because 2, 18 and 6 are all divisible by #color(red)(2)# we can still factor the terms:

#(color(red)(2)(x - 9))/(color(red)(2) xx 3)#

#(color(purple)(cancel(color(red)(2)))(x - 9))/(color(purple)(cancel(color(red)(2))) xx 3)#

#(x - 9)/3#