Divide numerator and denominator by the numerator x-4

Either long division or by synthetic division:

            x² -  3x - 10
x - 4)x³ - 7x² +  2x + 40
      x³ - 4x²
          -3x² +  2x
          -3x² + 12x
                -10x + 40
                -10x + 40

or  

4 | 1 -7   2  40
  |    4 -12 -40
    1 -3 -10   0

either way the denominator factors as



Then as long as x is not 4, we can cancel (x-4)





You can leave it like that or factor the denominator:



Edwin