Question 1006591
Honestly, {{{(x+2)/(x-2)}}} is a perfectly valid answer. If I were grading your homework, then I would accept that answer.


Here's what they did to get {{{1+4/(x-2)}}}


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{{{(x+2)/(x-2)}}}


{{{(x+2+2-2)/(x-2)}}} Notice the +2-2 up top. This is equal to 0. Adding 0 doesn't change the expression


{{{(x-2+2+2)/(x-2)}}} move the -2 next to the x to get "x-2"


{{{((x-2)+(2+2))/(x-2)}}}


{{{((x-2)+(4))/(x-2)}}}


{{{(x-2)/(x-2)+4/(x-2)}}} Break up the fraction using the rule {{{(a+b)/c = a/c + b/c}}}


{{{1+4/(x-2)}}} Use the rule {{{x/x = 1}}} (x is nonzero)



So that shows how {{{(x+2)/(x-2)}}} is equivalent to {{{1+4/(x-2)}}}


Side Note: you can also use polynomial long division or synthetic division to find that {{{(x+2)/(x-2)=1+4/(x-2)}}}