Answer:
[tex] \frac{x - 4}{x - 3} [/tex]
Step-by-step explanation:
[tex] \frac{ {x}^{2} - 8x + 16 }{ {x}^{2} - 7x + 12} [/tex]
Lets split the numerator and denominator.
[tex] = > \frac{ {x}^{2} - 4x - 4x + 16}{ {x}^{2} - 3x - 4x + 12} [/tex]
Lets factorise the numerator and denominator.
[tex] = > \frac{x(x - 4) - 4(x - 4)}{x(x - 3) - 4(x - 3)} [/tex]
[tex] = > \frac{(x - 4)(x - 4)}{(x - 3)(x - 4)} [/tex]
Cancelling x - 4 from numerator and denominator ,
[tex] = > \frac{x - 4}{x - 3} [/tex]
