[tex]f(x)=\frac{9x^2-36}{3x+6}[/tex] If this is what you mean,
Notice clearly, we can factor 9x^2-36 out, same with 3x+6
[tex]f(x)=\frac{9(x^2-4)}{3(x+2)}\\f(x)=\frac{9(x+2)(x-2)}{3(x+2)}\\f(x)=\frac{9(x-2)}{3}\\\\f(x)=\frac{3(x-2)}{1}\\f(x)=3(x-2)\\f(x)=3x-6[/tex]
From x^2-4, use the Difference of Two Squares, [tex]x^2-y^2=(x+y)(x-y)[/tex]
To find the x-intercept, y or f(x) = 0
[tex]0=3x-6\\6=3x\\x=2[/tex]
Now we know the x-intercept. To find the y-intercept, x = 0 therefore,
[tex]f(0)=3x-6\\f(0)=3(0)-6\\f(0)=-6[/tex]
So point or dot at x = 2 and y = -6 then draw the line. It should be like the graph shown below (Image.)
