## Simplifying Rational Expressions: x2+7x+10/x2+11x+18

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

### Simplifying Rational Expressions: x2+7x+10/x2+11x+18

Hi everyone, my name is Leah and I'm taking an online College Algebra course at WCJC. I just need help understanding this question . Anything would be helpful.

Simplify the rational expression. Find all the numbers that must be excluded from the domain of the simplified rational expression.

x2 + 7x + 10/
x2 + 11x + 18

What i don't understand is the last part of the question, finding all the numbers that must be excluded. I know how to simplify rational expressions. Also it's multiple choice, so that kind of narrows it down, I just want to understand this.
Thanks.
leahlou

Posts: 1
Joined: Sat Jan 17, 2009 3:53 am

### Re: Simplifying Rational Expressions

leahlou wrote:Simplify the rational expression. Find all the numbers that must be excluded from the domain of the simplified rational expression.

x2 + 7x + 10/
x2 + 11x + 18

What i don't understand is the last part of the question, finding all the numbers that must be excluded. I know how to simplify rational expressions. Also it's multiple choice, so that kind of narrows it down, I just want to understand this.
Thanks.

Hi Leah, the section on Rational Expressions: Finding the Domain should help you understand this.

In a nutshell, however, they're asking for what value (or values) of $x$ would cause the denominator (the bottom half) of the simplified expression to equal zero and thus cause a 'division by zero', which is not allowed.

Also, the section on how to type math clearly will show you how to layout equations so that they appear correctly:

$\frac{x^2\,+\,7x\,+\,10}{x^2\,+\,11x\,+\,18}$

DAiv
DAiv

Posts: 44
Joined: Tue Dec 16, 2008 7:47 pm

leahlou wrote:Simplify the rational expression....

x2 + 7x + 10/
x2 + 11x + 18

To do the simplification on your own (that is, when there aren't multiple-choice options whose graphs you can compare), reduce this fraction just like you'd reduce any numerical fraction: Find the common factors, and divide them out (or, if you prefer, "cancel" them off).

Note: This requires that you know how to factor quadratics!

Have fun!

Eliz.

stapel_eliz

Posts: 1782
Joined: Mon Dec 08, 2008 4:22 pm