Question

Which expression is equivalent to the following complex fraction? X/x-3/x^2/x^2-9

A) x-3/x
B) x+3/1
C) x+3/x
D) x/x+3

Answer 1

c

Explanation:

Answer 2

C)
`(x+3)/(x)`

Explanation:

The given expression is

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

We rewrite to obtain:

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

Multiply the first fraction by the reciprocal of the second to get;

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

Factor the numerator using difference two squares;

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

`(x)/(x-3) * ((x-3)(x+3))/(x^2)`

Cancel out the common factors to get;

`(1)/(1) * ((1)(x+3))/(x)`

This simplifies to;

`(x+3)/(x)`