Question

We need to find the numerator and denominator of the quotient.

Answer 1

Answer:

$\dfrac{(x - 2)^2}{(x - 1)^2}$

Step-by-step explanation:

$\dfrac{x^2 + x - 6}{x^2 - 6x + 5} \div \dfrac{x^2 + 2x - 3}{x^2 - 7x + 10} =$

$= \dfrac{x^2 + x - 6}{x^2 - 6x + 5} \times \dfrac{x^2 - 7x + 10}{x^2 + 2x - 3}$

$= \dfrac{(x + 3)(x - 2)}{(x - 1)(x - 5)} \times \dfrac{(x - 5)(x - 2)}{(x - 1)(x + 3)}$

$= \dfrac{(x + 3)(x - 2)(x - 5)(x - 2)}{(x - 1)(x - 5)(x - 1)(x + 3)}$

$= \dfrac{(x - 2)(x - 2)}{(x - 1)(x - 1)}$

$= \dfrac{(x - 2)^2}{(x - 1)^2}$