1)
a) \(\dfrac{x^3-x}{3x+3}=\dfrac{x\left(x^2-1\right)}{3\left(x+1\right)}=\dfrac{x\left(x+1\right)\left(x-1\right)}{3\left(x+1\right)}=\dfrac{x\left(x-1\right)}{3}\)
b) \(\dfrac{x^2+4y^2-4xy-4}{2x^2-4xy+4x}=\dfrac{\left(x-2y\right)^2-4}{2x\left(x-2y+2\right)}=\dfrac{\left(x-2y-2\right)\left(x-2y+2\right)}{2x\left(x-2y+2\right)}=\dfrac{x-2y-2}{2x}\)
c)\(\dfrac{10x-15}{4x^2-9}=\dfrac{5\left(2x-3\right)}{\left(2x-3\right)\left(2x+3\right)}=\dfrac{5}{2x+3}\)
2) (x4 + 2x3 + 10x - 25) : (x2 + 5)
= x2 + 2x - 5
3)
a) 16 - (x+3)2 = 0
<=>(4 - x - 3)(4+x+3) = 0
<=> \(\left[{}\begin{matrix}1-x=0\\7+x=0\end{matrix}\right.=>\left[{}\begin{matrix}x=1\\x=-7\end{matrix}\right.\)
b) x2 - x - 6 = 0
<=> x2 + 2x - 3x - 6 = 0
<=> x(x+2) - 3(x+2) = 0
<=> (x-3)(x+2) = 0
<=> \(\left[{}\begin{matrix}x-3=0\\x+2=0\end{matrix}\right.=>\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
