Question

which expression is in simplest form?

1. \\(\frac{x}{x^2}\\)
2. \\(\frac{9}{x^2 + 9}\\)
3. \\(\frac{x^2 - 4}{x + 2}\\)
4. \\(\frac{x^2 - 6x + 9}{x^2 - x - 6}\\)

Explanation:

Step1: Simplify Option 1

$\frac{x}{x^2} = \frac{1}{x}, x
eq0$

Step2: Check Option 2

$x^2+9$ cannot be factored over real numbers, so $\frac{9}{x^2+9}$ cannot be simplified further.

Step3: Simplify Option3

$\frac{x^2-4}{x+2}=\frac{(x-2)(x+2)}{x+2}=x-2, x
eq-2$

Step4: Simplify Option4

$\frac{x^2-6x+9}{x^2-x-6}=\frac{(x-3)^2}{(x-3)(x+2)}=\frac{x-3}{x+2}, x
eq3,-2$

Answer:

1. $\boldsymbol{\frac{9}{x^2+9}}$