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

1 Answer
Apr 8, 2018

Answer:

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.