Find the limit.

lim x→1 x^4-5x^3+7x^2-6x+3 / x-1

lim (x^4-5x^3+7x^2-6x+3)/(x-1) as x->1

Note that if we substitute 1 to the function, the denominator becomes zero (and we don't want that). But take note that the numerator can be factored:
lim (x-1)(x^3 - 4x^2 + 3x - 3) / (x-1)
Thus the x-1 will be cancelled, and we'll left with:
lim (x^3 - 4x^2 + 3x - 3) as x->1
Now we can substitute x = 1:
= 1^3 - 4*1^2 + 3*1 - 3
= 1 - 4 + 3 - 3
= -3

If you had a hard time factoring long and complicated polynomials, you may also use L'Hopital's rule (though this requires knowledge on differentiation).

Hope this helps~ :3