zad. 4
a)
\frac{a}{x}+\frac{b}{y}=\frac{ay+bx}{xy}
x\neq0, y\neq0
b)
\frac{4x+1}{x^2-3x}-\frac{5}{2x-6}=\frac{4x+1}{x(x-3)}-\frac{5}{2(x-3)}=\frac{2(4x+1)-5x}{2x(x-3)}=\frac{3x+2}{2x(x-3)}
x\neq0, x\neq3
Zad. 5
W(x)=x^4+2x^3+ax^2-6x
W(-2)=(-2)^4+2(-2)^3+a*(-2)^2-6*(-2)=16-16+4a+12=4a+12
4a+12=0
4a=-12
a=-3
W(x)=x^4+2x^3-3x^2-6x
(x^4+2x^3)-(3x^2+6x)=x^3(x+2)-3x(x+2)=(x+2)(x^3-3x)=x(x^2-3)(x+2)=
=x(x-\sqrt3)(x+\sqrt3)(x+2)
Odp
x=0, x=\sqrt3, x=-\sqrt3, x=-2