Question

How do you simplify `(x^2-3)/(x^2-4x+3)`?

Answer 1

It is simplified

Explanation:

Given: `(x^2 - 3)/(x^2 - 4x + 3)`

Factor both the numerator and denominator to see if anything can be cancelled.

For the numerator, use the difference of squares: `(a^2 - b^2) = (a - b)(a + b)`

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

`(x^2 - 3)/(x^2 - 4x + 3) = ((x + sqrt(3))(x - sqrt(3)))/((x-1)(x-3))`

Nothing can be cancelled. This means `(x^2 - 3)/(x^2 - 4x + 3)` is in simplest form.