Question

{x^{2}-8x+16 }{x^{2}-7x+12 }" alt="\frac{x^{2}-8x+16 }{x^{2}-7x+12 }" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$\frac{x - 4}{x - 3}$

Step-by-step explanation:

$\frac{ {x}^{2} - 8x + 16 }{ {x}^{2} - 7x + 12}$

Lets split the numerator and denominator.

$= > \frac{ {x}^{2} - 4x - 4x + 16}{ {x}^{2} - 3x - 4x + 12}$

Lets factorise the numerator and denominator.

$= > \frac{x(x - 4) - 4(x - 4)}{x(x - 3) - 4(x - 3)}$

$= > \frac{(x - 4)(x - 4)}{(x - 3)(x - 4)}$

Cancelling x - 4 from numerator and denominator ,

$= > \frac{x - 4}{x - 3}$