Question

Efectuati:$a) \frac{x+2}{ x^{2} -3x+2}+ \frac{x+1}{ x^{2}-4x+3 }+ \frac{x^{3}-5 x^{2}+x+11 }{ x^{3}-6 x^{2}+11x-6 } =$

Answer 1

x²-3x+2= (x-2) (x-1)
x²-4x+3 = (x-1) (x-3)
x³-6x²+11x-6= (x-1)(x-2)(x-3)
=> ecuatia este egala cu : (x+2)*(x-3) + (x+1)*(x-2)+(x³-5x²+x+11) totul supra (x-1)*(x-2)*(x-3)
= x²-x-6 + x²-x-2 + x³-5x²+x+11 totul supra (x-1)*(x-2)*(x-3)=
= x³-3x²-x+3 totul supra (x-1)*(x-2)*(x-3)=
=(x-1)*(x²-2x-3) totul supra (x-1)*(x-2)*(x-3) =
= x²-2x-3 totul supra (x-2)*(x-3)