How do you simplify $\frac{x^{2} - 2 x - 3}{x^{2} - 7 x + 12}$ $(x^2-2x-3)/(x^2-7x+12)$ ?

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Answer 1 · 2017-08-18T13:41:15

See a solution process below:

First, we can factor the numerator and denominator as follows:

$\frac{(x - 3) (x + 1)}{(x - 3) (x - 4)}$ $((x - 3)(x + 1))/((x - 3)(x - 4))$

We can now cancel common terms in the numerator and denominator:

$(color(red)(cancel(color(black)((x - 3))))(x + 1))/(color(red)(cancel(color(black)((x - 3))))(x - 4)) => (x + 1)/(x - 4)$

However, from the original expression we need to ensure we don't divide by $0$ .

$(x + 1)/(x - 4)$ Where $x - 4 != 0$ and $x - 3 !=0$

Or

$(x + 1)/(x - 4)$ Where $x != 4$ and $x != 3$

How do you simplify (x^2-2x-3)/(x^2-7x+12)x2−2x−3x2−7x+12(x^2-2x-3)/(x^2-7x+12)?