Adding and Subtracting Rational Expressions?

Question

Find the least common denominator for each group of rational expressions.


5 over 18x^2y^3 , -3 over 24x^4y^5


9 over k+3 , 3 over k


17 over 3r-21 , 9 over r-7


x over x^2 - 81 , 3x over x^2+18x +81

Answer 1

18x^2y^3 and 24x^4y^5, common factor is 6x^2y^3
remaining factors are 3 and 4x^2y^2, so the least common denominator is
3(6x^2y^3)(4x^2y^2) = 72x^4y^5

k+3 and k, no common factors; least common denominator is k(k+3).

3r-21, r-7: 3r-21 = 3(r-7), so least common denominator is 3r-21.

x^2 - 81, x^2 + 18x + 81: factorise as
(x-9)(x+9) and (x+9)^2 respectively
=> common factor of x+9, least common denominator is (x-9)(x+9)^2.