Answer:
[tex]x-5[/tex]
Step-by-step explanation:
Consider the expression
[tex]\dfrac{3x^3-15x^2+15x-75}{3x^2+15}[/tex]
Its numerator [tex]3x^3-15x^2+15x-75[/tex] is equivalent to
[tex]3x^3-15x^2+15x-75\\ \\=3x^2(x-5)+15(x-5)\\ \\=(x-5)(3x^2+15)[/tex]
Therefore, given expression can be rewritten as
[tex]\dfrac{(x-5)(3x^2+15)}{3x^2+15}=x-5[/tex]
Note that [tex]3x^2+15\neq 0,[/tex] so we can divide the numerator and the denominator by non-zero expression [tex]3x^2+15.[/tex]
