#(x^2-5x-6)/(x^3+ax^2+bx+c)# simplifies to #1/(x-2)#, then a+b+c = ?

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Answer 1 · 2017-11-09T17:04:25

#a + b + c = 9#

Given: #(x^2-5x-6)/(x^3+ax^2+bx+c) = 1/(x-2)#

It follows that:

#(x^2-5x-6)(x-2)=x^3+ax^2+bx+c#

Multiply

#x(x^2-5x-6) - 2(x^2-5x-6) = x^3+ax^2+bx+c#

#x^3-5x^2-6x - 2x^2+10x+12 = x^3+ax^2+bx+c#

Combine like terms:

#x^3-7x^2+4x+12 = x^3+ax^2+bx+c#

Match coefficients:

#a = -7, b = 4, and c = 12#

#a + b + c = -7+ 4 + 12#

#a + b + c = 9#