How do you simplify #4/(x-2)-3/(x+1)+2/(x^2-x-2)#?

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Answer 1 · 2017-01-18T09:37:51

#(x+12)/((x-2)(x+1))=(x+12)/(x^2-x-2)#

#4/(x-2)-3/(x+1)+2/(x^2-x-2)#

We need the denominators to be the same. We can do that by multiplying through with various forms of the number 1:

#4/(x-2)(1)-3/(x+1)(1)+2/((x-2)(x+1))#

#4/(x-2)((x+1)/(x+1))-3/(x+1)((x-2)/(x-2))+2/((x-2)(x+1))#

#(4(x+1))/((x-2)(x+1))-(3(x-2))/((x+1)(x-2))+2/((x-2)(x+1))#

#(4x+4)/((x-2)(x+1))-(3x-6)/((x+1)(x-2))+2/((x-2)(x+1))#

#((4x+4)-(3x-6)+2)/((x-2)(x+1))#

#(4x+4-3x+6+2)/((x-2)(x+1))#

#(x+12)/((x-2)(x+1))=(x+12)/(x^2-x-2)#