Question

Find the least common denominator for these two rational expressions. x²/x²+2x+1 and 5/x²+4x+3

Answer 1

Factor each denominator:

x^2 + 2x + 1 = (x+1)^2

x^2 + 4x + 3 = (x+3)(x+1)

Now take the common and non common factors with the highest exponents and multiply them.

(x+3).(x+1)^2 is the least common denominator.

If you expand that product you will get x^3 + 5x^2 + 7x +3