Question

Calculati rapoartele din imaginea de mai jos, va rog mult !

Answer 1

a)
x/(x²-4x+4) · (x²-4)/x² =
=1/(x-2)² · (x+2)(x-2)/x =
=(x+2)/x(x-2)
b)
(x²-5x+4)/(x-5):(x-4)/(2x-10)=
=(x²-4x-x+4)/(x-5):(x-4)/2(x-5)=
=[x(x-4)-(x-4)]/(x-5)·2(x-5)/(x-4)=
=(x-4)(x-1)/1 ·2/(x-4)=
=2(x-1)
c)
((x²+5x)/(x²-4x+4) : (x²+7x+10)/(x²-4)=
=x(x+5)/(x-2)² : (x²+5x+2x+10)/(x+2)(x-2)=
=x(x+5)/(x-2)² : (x+5)(x+2)/(x+2)(x-2)=
=x(x+5)/(x-2)² · (x+2)(x-2)/(x+5)(x+2)=
=x/(x-2) 
d)
(x²-9)/(x²+7x+12) ·(x²+8x+16)/(x²-5x+6) : (5x+20)/(4x-8)=
=(x+3)(x-3)/(x²+4x+3x+12) ·(x+4)²/(x²-2x-3x+6) : 5(x+4)/4(x-2)=
=(x+3)(x-3)/(x+4)(x+3) ·(x+4)²/(x-2)(x-3) · 4(x-2)/5(x+4)=
=(x-3)/(x+4) ·(x+4)²/(x-2)(x-3) · 4(x-2)/5(x+4)=4/5

e)
(4x-12)/(x²-9) -(x+2)/(x-3) : (x²+5x+6)/(x-3) =
=4(x-3)/(x+3)(x-3) -(x+2)/(x-3) : (x²+2x+3x+6)/(x-3) =
=4/(x+3) -(x+2)/(x-3) : (x+2)(x+3)/(x-3) =
=4/(x+3) -(x+2)/(x-3) · (x-3)/(x+2)(x+3) =
=4/(x+3) - 1/(x+3) =
=3/(x+3)