What is x-3 divide by 4x squared -10x plus 2?

Answer 1

Do the long division by removing the highest power of x at each stage:

_________________2x_+_6

_______---------------------

_2x-1_|_4x²_+_10x_-_4

_________4x²_-___2x

_________-------------

_________________12x_-_4

_________________12x_-_6

_________________----------

________________________2

→ (4x² + 10x - 4) ÷ (2x - 1) = 2x + 6 remainder 2.

Checking:

(2x + 6)(2x - 1) + 2 = 4x² -2x + 12x - 6 + 2 = 4x² + 10x - 4 = dividend.

Answer 2

There is no simplification because there are no common factors. So the answer is

(x-3)/[2*(2x2-5x+1)]