Question

E(x) =(2x²-7x-17/ x+1) 1
-------------- - ----- : --------- = (x+2)(x+3)

x²-10x+21 x-7 x²-9

Answer 1

x²-10x+21=x²-7x-3x+21=x(x-7)-3(x-7)=(x-7)(x-3)
x²-9=(x-3)(x+3)

E(x)=[(2x²-7x-17)/(x²-10x+21) - (x+1)/(x-7)]:1/(x²-9)=
=[(2x²-7x-17)/(x-7)(x-3) - (x+1)/(x-7)] ×(x-3)(x+3)=
=[(2x²-7x-17) - (x+1)(x-3)]/(x-7)(x-3) ×(x-3)(x+3)=
=(2x²-7x-17 - x²-x+3x+3)/(x-7) ×(x+3)=
=(x²-5x-14)/(x-7) ×(x+3)=
=(x²-7x+2x-14)/(x-7) ×(x+3)=
=[x(x-7)+2(x-7)]/(x-7) ×(x+3)=
=(x-7)(x+2)/(x-7) ×(x+3)=
=(x+2)(x+3)