# Rational algebraic expressions

So we can rewrite this up here. Section : Rational Expressions We now need to look at rational expressions. We have x plus 3 times x minus 3. If we were to multiply this times each of these terms, you get that right there. In this case, it's a variable expression. If we make the 9 positive and we make the b negative 6, it works. That's this term right here.

Rational expressions are essentially the same thing, but instead of the numerator being an actual number and the denominator be an actual number, they're expressions involving variables. In fact, because of that the work will be slightly easier in this case.

But for them to really be equal, we have to add the condition.

## Rational expressions and equations

This is 2x squared plus 5x minus 3. We can rewrite this as 3x squared, and I'm going to say plus 9x minus 6x minus Example 1 Reduce the following rational expression to lowest terms. In this case the least common denominator is Notice, all I did here is I split this 3x into a 9x minus 6x. We are now at that exception. There is an unspoken rule when dealing with rational expressions that we now need to address. And normally, I decide which term goes with which based on what's positive or negative or which has common factors. This is 5 times x plus 3. So this is a positive 1, right?

One of them simply has a denominator of one. Do NOT write down the power that is on each factor, only write down the factor Now, for each factor written down in the previous step write down the largest power that occurs in all the denominators containing that factor.

And the two obvious numbers here are 2 and 3. So let's factor out a 3x out of this expression on the left.

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