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

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Answer 1 · 2017-04-07T13:01:49

#= (4(x+1))/(x(x+2))#

In order to simplify two fractions you need to convert both fractions to a common denominator (which in this case is #x(x+2)#)

#(x+2)/x xx color(red)((x+2)/(x+2)) - x/(x+2) xx color(red)(x/x)#

#= ((x+2)(x+2) - x xx x)/(x(x+2)#

#= (x^2 +4x +4 -x^2)/(x(x+2)#

#= (4x+4)/(x(x+2)#

#= (4(x+1))/(x(x+2))#

NOTE:
Both #color(red)((x+2)/(x+2)) and color(red)(x/x)# are equal to #color(red)(1)#

Multiplying by 1 does not affect the value of an expression, just what it looks like.