Week One Discussion
Domains of Rational Expressions

The first initial of my first name is G and these are my assigned rational expression on which to base my work:

x2-14x+49100x | m2+2m-24m2-3m |

The domain of a rational expression is the set of all real numbers except the value/values of the variable that result in division by zero when substituted into the expression.

In the Real Number System division by zero cannot be done. There is no number that can be the answer when divided by zero this attempt would be called “undefined.” A denominator cannot be zero since in a rational expression the denominator divides the numerator.

In my first expression, I need to set the denominator equal to zero to find my excluded values for x.
100x = 0 x= 0 This is the excluded value for my first expression.
The domain (D) for my first expression is the set of all Reals excluding ±0. In set notation, this can be written as D = {w| w ∈ ℜ, w ≠ 0}
In my second expression, I need to set the denominator equal to zero to find my excluded values for m. m2-3m= 0 I can simplify m(m-3)=0 Solving for m m= 0, 3 These are the excluded values for my second expression.
The domain (D) for my second expression is the set of all Reals excluding ±0,3 . In set notation, this can be written as D = {w| w ∈ ℜ, w ≠ 0,3}

Now, both of my expressions have excluded values. In one expression, I have one excluded value because zero times anything gives you zero and can not be in the denominator.. In the other expression, there are two excluded numbers because both, if inserted in place of the variable, would cause the denominator to become zero and thus the whole expression would become undefined