You need common a denominator. That is something that each of the separate denominators will divide into without having a remainder (fractional component)
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Consider the denominators od #x, x^2 " and " x+x^2#
#x+x^2" "#will divide into itself
#x^2# will not divide into #x+x^2# without a remainder. So we build something it will divide into. That is #x^2(x+x^2)#
#x# will divide into the #x^2# part of #x^2(x+x^2)#
#color(red)("Using " x^2(x+x^2) " as the common denominator we have:")#
For #1/x# we need to make this look like #("something")/(x^2(x+x^2))# but without changing its true value. This is done by multiplying by 1 but in the form of #(x(x+x^2))/(x(x+x^2)) #
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For #color(blue)(1/x)# we have #1/x times (x(x+x^2))/(x(x+x^2)) = color(blue)((x(x+x^2))/(x^2(x+x^2)))#
For #color(blue)(2/x^2)# we have #2/x^2 times (x+x^2)/(x+x^2) =color(blue)((2(x+x^2))/(x^2(x+x^2)))#
For #color(blue)(3/(x+x^2))# we have #3/(x+x^2) times x^2/x^2 =color(blue)((3x^2)/(x^2(x+x^2))#
Putting it all together
#color(blue)((x(x+x^2) +2(x+x^2)+3x^2)/(x^2(x+x^2)))#
