What is the least common denominator for the rational expressions 1⁄(x^2-5x-6) and 1⁄(x^2-12x+36) ? show your work.

Question

What is the least common denominator for the rational expressions 1⁄(x²-5x-6) and 1⁄(x²-12x+36) ? show your work.

Answer 1

1/(x² - 5x - 6) factors to 1/(x - 6)(x + 1)

1/(x² - 12x + 36) factors to 1/(x - 6)(x - 6) or 1/(x - 6)²

So the common denominator would be divisible by (x + 1), (x - 6) and (x - 6)². That would be (x + 1)(x - 6)².