Make a sign chart (y-chart) for the function
y=(-1)(x)/(x-3)
by making each factor a row and the zeros of each factor forming the columns across the top in number line order:
color(white)(aaaaaaaaaaaaaaaacolor(black)(0)aaaaaaaaacolor(black)(3)aaaaa
(-1)color(white)(aaaacolor(black)((-))aaaaaaacolor(black)((-))aaaaaaacolor(black)((-))
color(white)(aa)xcolor(white)(aa.aaacolor(black)((-))aaaaaaacolor(black)((+))aaaaaaacolor(black)((+))
(x-3)color(white)(aaacolor(black)((-))aaaaaaacolor(black)((-))aaaaaaacolor(black)((+))
color(white)(aaaaaaaaaaaaaaaaaaaaaa)/color(white)(aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa)
color(white)(aaa)ycolor(white)(aaaaacolor(black)((-))aaaaaaacolor(black)((+))aaaaaaacolor(black)((-))
The sign of the y-value in the bottom row comes from the product of the factors above. ( - ) (- )( - ) = (- ) , (-)(-) = (+), and so on.
From the chart it is clear that the function is positive in the interval from zero to 3, and since the inequality is ">= 0," the endpoints are included. Thus the solution is the values of x where 0<=x<=3.
