Question

Simplify x^2-9 over x^2-3x

Answer 1

`x^(2) -3x-(9)/(x^(2) )`

Explanation:

`x^(2) -9` ÷
`x^(2) -3x`

To add or subtract expressions, expand them to make their denominators the same. Multiply
`x^(2) -3x` times
`(x^(2) )/(x^(2) )`

-

`((x^(2) -3x)x^(2) )/(x^(2) ) - (9)/(x^(2) )`

Since
`((x^(2) -3x)x^(2) )/(x^(2) )` and
`(9)/(x^(2) )` have the same denominator, subtract them by subtracting their numerators.

-

`((x^(2) -3x)x^(2) -9)/(x^(2) )`

Do the multiplications in
`(x^(2) -3x)x^(2) -9`

-

`(x^(4)-3x^(3)-9 )/(x^(2) )`

Answer 2

`(x+3)/(x)` or x+3/x

Explanation:

Using D.O.T.S (difference of two squares) formula :

`a^(2) -b^(2) = (a+b)(a-b)`

`x^(2) -9= (x+3)(x-3)`

Factorise the second bit:

`x^(2) -3x = x(x-3)`

Now write out this fraction:

`((x+3)(x-3))/(x(x-3))`

Now we can cancel out repeated terms (x-3):

`((x+3))/(x)`
This is our final answer:

`(x+3)/(x)`