Question

Exercitiul 8 va rog !

Answer 1

a)(x²-9x+14)/(x²-4)=(x²-7x-2x+14)/(x-2)(x+2)=[x(-7)-2(x-7)]/(x-2)(x+2)=
=(x-7)(x-2)/(x-2)(x+2)=(x-7)/(x+2)

b)(x²+8x+12)/(x²+7x+6)=(x²+6x+2x+12)/(x²+6x+x+6)=
=[x(x+6)+2(x+6)]/[x(x+6)+(x+6)]=(x+6)(x+2)/(x+6)(x+1)=(x+2)/(x+1)

c) (4-x²)/(x²+10x+16)=(2-x)(2+x)/(x²+2x+8x+16)=(2-x)(2+x)/(x+2)(x+8)=
=(2-x)/(x+8)

d)(x²+3x-4)/(x²-5x+4)=(x²+4x-x-4)/(x²-x-4x+4)=(x+4)(x-1)/(x-1)(x-4)=
=(x+4)/(x-4)

e) (9-x²)/(x²-8x+15)=(3-x)(3+x)/(x²-3x-5x+15)=(3-x)(3+x)/(x-3)(x-5)=
=(x-3)(3+x)/(x-3)(5-x)=(3+x)/(5-x)

f) (x³-x)/(x²-2x+1)=x(x²-1)/(x-1)²=x(x-1)(x+1)/(x-1)²=x(x+1)/(x-1)

g)[x(x-2)+1]/(x²+2x-3)=(x²-2x+1)/(x²+3x-x-3)=(x-1)²/(x+3)(x-1)=(x-1)/(x+3)

h)(x²-x-6)/[(x-4)²+(x-4)]=(x²+2x-3x-6)/(x-4)(x-4+1)=(x+2)(x-3)/(x-4)(x-3)=
=(x+2)/(x-4)