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

Apr 8, 2018

It is simplified

Explanation:

Given: $\frac{{x}^{2} - 3}{{x}^{2} - 4 x + 3}$

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

For the numerator, use the difference of squares: $\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$

$\left({x}^{2} - 3\right) = {x}^{2} - {\left(\sqrt{3}\right)}^{2} = \left(x + \sqrt{3}\right) \left(x - \sqrt{3}\right)$

$\frac{{x}^{2} - 3}{{x}^{2} - 4 x + 3} = \frac{\left(x + \sqrt{3}\right) \left(x - \sqrt{3}\right)}{\left(x - 1\right) \left(x - 3\right)}$

Nothing can be cancelled. This means $\frac{{x}^{2} - 3}{{x}^{2} - 4 x + 3}$ is in simplest form.