# Math Help - Simplify Rational Expression

1. ## Simplify Rational Expression

simplify each rational expression. find all numbers that must be excluded from the domain of the simplified rational expression.

y^2 + 7y - 18 / y^2 - 3y + 2

got it down to

y + 9 / y - 1

y cannot equal 1

the answer in the book says y cannot equal 1 or 2. why the 2?

2. ## Re: Simplify Rational Expression

Originally Posted by PaperStSoap
simplify each rational expression. find all numbers that must be excluded from the domain of the simplified rational expression.

y^2 + 7y - 18 / y^2 - 3y + 2

got it down to

y + 9 / y - 1

y cannot equal 1

the answer in the book says y cannot equal 1 or 2. why the 2?
Assuming that your expression is \displaystyle \begin{align*} \frac{y^2 + 7y - 18}{y^2 - 3y + 2} \end{align*} (please use brackets where they're needed, or else learn some LaTeX), then we have

\displaystyle \begin{align*} \frac{y^2 + 7y - 18}{y^2 - 3y + 2} &\equiv \frac{(y + 9)(y - 2)}{(y - 1)(y -2)}\textrm{ with }y \neq \{1, 2\} \textrm{ since the denominator can not be 0} \\ &\equiv \frac{y + 9}{y - 1} \textrm{ with } y \neq \{ 1, 2\} \end{align*}

Basically you need to take into account all restrictions implied by the ORIGINAL definition of your function.

3. ## Re: Simplify Rational Expression

got it. thanks for the prompt answer.