Answer:
The simplified value is a+3.
Solution:
We need to solve, [tex]a-\frac{9}{a} \ divided\ by \ 1-\frac{3}{a}[/tex]
Simplifying we get,
[tex]\Rightarrow \frac{a-\left(\frac{9}{a}\right)}{1-\left(\frac{3}{a}\right)}[/tex]
[tex]\Rightarrow \frac{\frac{a^{2}-9}{a}}{\frac{a-3}{a}}[/tex]
[tex]\Rightarrow \frac{a^{2}-9}{a-3}[/tex]
[tex]\Rightarrow \frac{a^{2}-3^{2}}{a-3}[/tex]
[tex]\Rightarrow \frac{(a+3)+(a-3)}{a-3}[/tex] [tex](//as \ we \ know \ that \ (a^2 - b^2) = (a+b)\times(a-b))[/tex]
[tex]\Rightarrow (a+3) \times\left(\frac{a-3}{a-3}\right)[/tex]
[tex]\Rightarrow (a+3)[/tex]
