Question

Simplify a- 9/a divided by 1-3/a =

Answer 1

a+3

i took the test

Answer 2

The simplified value is a+3.

Solution:

We need to solve,
`a-(9)/(a) \ divided\ by \ 1-(3)/(a)`

Simplifying we get,

`\Rightarrow (a-\left((9)/(a)\right))/(1-\left((3)/(a)\right))`

`\Rightarrow ((a^(2)-9)/(a))/((a-3)/(a))`

`\Rightarrow (a^(2)-9)/(a-3)`

`\Rightarrow (a^(2)-3^(2))/(a-3)`

`\Rightarrow ((a+3)+(a-3))/(a-3)`
`(//as \ we \ know \ that \ (a^2 - b^2) = (a+b)*(a-b))`

`\Rightarrow (a+3) *\left((a-3)/(a-3)\right)`

`\Rightarrow (a+3)`