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

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Answer 1 · 2018-04-08T19:48:17

It is simplified

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.

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