Polynomial and Rational Expressions

Question

Simplify the expression

x^2 - 10x + 21 / x^3 - 13x^2 + 42x

Answer 1

To solve the following equation:

x^2 - 10x + 21 / x^3 - 13x^2 + 42x

The first thing I would do is try to factor both the top & bottom, and see if anything cancels out, which would simplify this expression. This yields: (x-3)(x-7) , which can be simplified to : (x-3)(x-7).

x (x²-3x+42) x (x-6)(x-7)

Now we can can out the (x-7) from the top & bottom, leaving us with: (x-3)/x(x-6).

Tip for solving equations (in general). Remember to use the Order of Operations, which you can remember by the following sentence: Please Excuse My Dear Aunt Sally, which stands for:

P parenthesis, E exponents, M multiply, D divide, A add, S subtract!!

Answer 2

(x^2 - 10x + 21) /(x^3 - 13x^2 + 42x) = (x - 3)(x - 7)/[x(x - 7)(x - 6) = (x - 3)/(x² - 6x)