Rational expressions (add and subtract)

Question

Suppose we wanted to add the following rational expressions. Only the denominators are shown.

?/x²-4x-5 + ?/x²-3x-4 - ?/x²-9x+20

What would the common deonominator be? (The common denominators are above the denominators. The common denominators are unknown with '?')

Answer 1

The wording and syntax is problematic. I assume you mean 1/(x²-3x-4)...

If so, you need to factor each denominator in order to find the least common denominator:

(x-5)(x+1), (x-4)(x+1), and (x-4)(x-5)

If you add these fractions (1/whatever), the ? would be the numerators obtained by putting the fractions in terms of the common denominator

((x-4) + (x-5) + (x+1))/((x-5)(x-4)(x+1))

I hope that addresses your problem.