Simplify

We have

$\,\dfrac{3^{x}+63}{21^{x-2}+7^{x-1}}=\dfrac{9\times 3^{x-2}+63}{3^{x-2}\times 7^{x-2}+7\times 7^{x-2}}\\ \qquad\qquad\qquad=\dfrac{9\times (3^{x-2}+7)}{7^{x-2}\times (3^{x-2}+7)}\\ \qquad\qquad\qquad=\dfrac{9}{7^{x-2}}\\ \qquad\qquad\qquad=\dfrac{9\times 49}{7^{x}}$

So the correct answer is $\dfrac{9\times49}{7^{x}}$ .

Since this is a multiple choice question, I substitude x = 2, then i get the answer.

We can easily get through this by substituting x= 2, On the question part and then on the given options. When we substitute x= 2 we will get 9 from question part likewise we will get same ans from the choices. That will be the correct one

441(3^x+69)/7^x(3^x+63)=441/7^x=9 X 49/7^x