ANSWER:
The quotient of (pic) has __x² + 4 - 4x__ in the numerator and ___x² + 1 - 2x___ in the denominator.
EXPLANATION:
–» x² + x - 6/x² - 6x + 5 ÷ x² + 2x - 3/x² - 7x + 10
–» x² + x - 6/x² - 6x + 5 × x² - 7x + 10/x² + 2x - 3
–» x² + 3x - 2x - 6/x² - 5x - x + 5 × x² - 5x - 2x + 10/x² + 3x - x - 3
–» x(x + 3) - 2(x + 3)/x(x - 5) - 1(x - 5) × x(x - 5) - 2(x - 5)/x(x + 3) - 1(x + 3)
–» (x - 2)(x + 3)/(x - 1)(x - 5) × (x - 2)(x - 5)/(x - 1)(x + 3)
–» (x - 2)/(x - 1) × (x - 2)/(x - 1)
–» (x - 2)²/(x - 1)²
–» x² + 4 - 4x/x² + 1 - 2x.
